# Estimation Question

Case Interview Example - Estimation Question and Answer

I was asked the following management consulting estimation question by a McKinsey interviewer many years ago:

"Estimate how long it would take to move or relocate an average size mountain 10 miles using an average size truck"

Below you will see my answer to this estimation question and the process and rational I use to answer this specific question can be used as a template to practice answering other estimation questions as you prepare for case interviews.

The first thing to realize in an estimation question is that an acceptable answer MUST mention a specific number.

This question was how much time it takes to move an average mountain 1 mile (or something along those lines).

If the answer does not include a specific unit of time like X hours, Y days, Z years, then the answer is not acceptable.

By the way, I use the word "acceptable answer" instead of "correct answer" very deliberately.  The interviewer's evaluation in this type of question is in assessing the approach you took, not necessarily the specific answer you gave.

The next thing to the answer must include is that explicit assumptions must be made.

It is not possible to answer this question without making some assumptions. They key is to EXPLAIN to the interview that you are going to make some assumptions. Once you do and once you make a specific assumption, explain your rationale behind that assumption.

For example, when I was given this question. I knew that I needed to estimate the cubic volume of the mountain. And since the mountain loosely resembles a cone, I knew there was a geometric formula to calculate the volume of a cone--except I did not recall the specific formula off the top off my head.

So my interviewer suggested that I estimate the formula of a cone, which in turn I would use to estimate the volume of an average size mountain, which would then be part of a calculation to estimate the average time it would take to re-locate it.

Notice the estimate that is nested within the estimate here. This is very common. Most important thing is to not get mixed up and confused by your own work.

I find it is useful to just write out the formula that will produce the estimate FIRST, THEN go about making reasonable assumptions.

For the move the mountain case, the formula I wrote up on the white board during my interview was:

volume of mountain / volume of a truck * time per truck trip = total time to move a mountain

I would literally write that on the board. That is the amount of time it would take 1 truck to move an average size mountain 10 miles (the 1 truck is an assumption as well)

Then I went about estimating each of those 3 factors.

Assume the average size mountain is 1 mile tall, 1 mile wide, and the shape of a cone. That's approximately 5,000 ft in height and base.

I forge the formula to calculate the volume of a cone, but if I eye ball it, it is probably a little more volume than half of a cube of similar size height and base.

The volume of a cube that's 5,000 ft tall, 5,000 ft wide, and 5,000 ft deep is 125,000,000,000 cubic ft.

Since I'm trying to estimate a CONE, and not a CUBE, I'd then take 125,000,000,000 x 50% (my approximate guess as to how much smaller a cone is vs a cube of approximately the same height, and width and length at the base.

With some slight rounding, that gets us 60,000,000,000.

Then underneath my original formula, I would write the following:

60,000,000,000 cubic ft / volume of a truck * time per truck trip = total time to move mountain

Next, I would move on to estimate the volume of a truck.

The carrying capacity of a cargo truck is the width x length x heightof the cargo container.

I said, well I know those big trucks are a little wider than my car, but not by much since they still must be able to fit into a lane on the freeway. My car sits 3 people across, assuming 2 ft in shoulder width per person, that's 6 ft of interior space. Let’s add on a little more and assume those big trucks are around 8 ft in width.

I know they are about double the length of most passenger sedans. And lets see if I were to lie down in the driver's seat to take a nap, I cover most of the interior cabin space. And the hood and trunk of the car combined are about the same length as the interior cabin. I'm a little under 6ft tall, so that makes my car around 12 ft long. If I double that, I get the length of one of those trucks to be 24 ft long. I subtract out say 4 ft for the driver compartment, and that leaves me about 20 ft in length for the cargo area.

Last time I looked, I saw a worker standing in the back of one of the cargo areas, and the cargo area was taller than the person. I figure the cargo container is about 8 ft tall. And since most freeway bridges have signs that say "height 13 ft" and I know those trucks can go under those bridges, assuming an 8ft cargo section and a 4ft for the tires and chassis under the cargo area, that gives me 12 ft...which does seem to triangulate with the height of those underpasses. So I'll say the cargo section is approximately 8 ft tall.

The volume of the cargo area of an earth moving truck is:

8 ft wide x 20 ft long x 8 ft tall = 1,280 cubic feet

For sake of simplicity, I'm going to round that down to 1,250 cubic feet and plug this number back into my original formula which now reads as follows:

60,000,000,000 cubic foot mountain / 1,250 cubic foot truck capacity * time for truck trip = total time to move a mountain

The only factor missing in our estimate is figuring out the round-trip time for a trip to move 10 miles, drop its load, and return the 10 miles. Let’s figure out the travel time first.  Assume the truck travels on the freeway at 60 miles per hour.

For it to travel 10 miles, it does so in 1/6 and hour or 10 minutes. The drive time is 10 minutes to the new location, and 10 minutes returning to the old mountain for a total of 20 minutes. Assume that the off-loading process has been designed to be pretty quick. The load is just "dropped" and then repositioned while the truck is on its return trip (as opposed to being scooped out of the truck, one scoop at time which seems more time consuming).

That means each round trip takes 30 minutes or 0.5 hours.

Let's go back to our formula again and update it.

60,000,000,000 cubic ft mountain / 1,250 cubic foot track capacity * 0.5 hours per truck trip = total time to move a mountain

Let me do the math now. For the first 2 components of the formula, that works out to about 50,000,000 (50 million truck loads).

50 million truck loads x 0.5 hours, thats 25 million hours to move a mountain.

If we assume a typical day has 25 hours (to make our math a little simpler), that's 1 million days to move the mountain using only 1 truck. That works out to a bit under 3,000 years

That is the logic I just presented is a pretty good one that would most likely pass most estimation question interviews.

You will notice that for every little component I explain WHY I felt that was a reasonable assumption.

There is a big difference between making a wild assumption vs. a reasonable one. Your goal is to make as reasonable assumption as you can come up with. When you make such an assumption, it is very important you explain WHY you made the assumption you did.

The math is not that complicated (it's math we all learned before high school) BUT communicating what you are doing is just as important.

It is also important that you do not make a math mistake. I wrote out this example quickly and hopefully I did not make a math mistake.

If I did make a math mistake, I would full expect to get rejected even if I got the logic and assumptions largely right.

That's just the way it works. Practice your mental math. You DO use it a lot not just in interviews but with clients as well.

501 comments… add one
• VA May 4, 2013, 10:02 pm

20000000 days

• RK May 10, 2013, 1:56 pm

In order to move estimate the time it takes to move a mountain 10 miles from one destination to another, the following information is required:

Total time = (Size of the mountain in kilograms/the amount of kilograms the truck is able to carry) x (Loading time+Unloading time+transition time)

1: Size of the mountain: Assuming the weight of the mountain is: 500.000.000.000 (pure guess)
2: Amount of kg the truck is able to carry: Estimated to be 5.000kg
3: Loading time: 1 hour
4: Unloading time: 1hour
5: Transition time: With a speed of 50 miles/hour – the truck is able to move from A to B and back again in 24 minutes (10 miles / 50 miles/hour = 0,2 => 60 minutes x 0,2 = 12 minutes => 12 minutes x 2 = 24 minutes)

Hence the total times is:
Total time = (Size of the mountain in kilograms/the amount of kilograms the truck is able to carry) x (Loading time+Unloading time+transition time)
=>
Total time = (Size of the mountain in kilograms/the amount of kilograms the truck is able to carry) x (60minutes + 60minutes + 24minutes)

Mountain size/Truck size = 500.000.000.000/5.000 = 100.000.000

Total time = (100.000.000) x (60minutes + 60minutes + 24minutes) = 100.000.000 x 144 minutes
To make it easy, I’ll round to 150 minutes

Total time needed: 100.000.000 x 150 = 15.000.000.000 Minutes => 15.000.000.000 minutes / 60minutes = 250.000.000 Hours

• Miaomiao May 14, 2013, 11:37 pm

* I am going to use international system of units
10miles=16km
Assume an average truck carry 4m*2m*2m=16m3 soil (estimated by the impression of truck size)
Assume the average speed of the truck is 32km/h (quite fair assumption..)
I guess the average mountain elevation is 200 meter
estimate the size of a mountain: (assume it’s a cone shape, the diameter is 200 meter, pi is 3)
The volume will be 100×100×3×200×1/3=2000000
* Assume 0 time for loading and unloading ( can be further modified)
It needs 2000000m3/16m3=125000times
For each time, it needs a round trip
16*2km/32km/h=1h/tim
Thus the total time is
125000hrs=14.3 years

• Luciano May 17, 2013, 3:16 pm

Let’s assume that an average size mountain is 500m high. If we think of that mountain as half a sphere, its volume is gonna be 4/3*pi*rˆ3, which is about 500 MM cubic meters.
Now, let’s assume we are working with a truck that can be loaded with 12 cubic meters (4*2*1,5) each time, and it takes about 5 minutes to load it and 5 minutes to unload it.
Also, let’s assume we’re gonna relocate that mountain to a place (point B) which is 1 km from the original one (point A). If the truck has an average speed of 20km/hours, it takes 3 minutes for the truck from point A to point B.
So, the total time spent for loading the truck, driving from point A to B and unloading the truck is 13 minutes.
Now, it takes about 42MM (500MM/12) trips from A to B to relocate the mountain. The time necessary to do that is gonna be 42MM * 13 minutes, which is 546 MM minutes, or little over 9MM hours.

• Jan Šimek May 20, 2013, 4:51 am

Presume, that average size truck can load 20 tuns and on 10 miles it is moving 30 miles/hour. The time for loading of the 20 tuns is 5 minutes and the same for unloading. To put it together, 20 tuns of ground takes total of 50 minutes (20 x 2 minutes of driving and 5 x 2 minutes of loading and unloading). The least known figure is the amount of ground in the hill. That can be calculated by knowledge of the height of the hill and how what is the size of the “base”, as well as how heavy is a m3. If the total weight of the hill is 200 000 tuns, then it takes 10 000 x 50 minutes = 500 000 minutes = 8 500 hours = 350 days = slightly less than a year.

• DL Jun 3, 2013, 7:06 pm

The question requires that a few assumptions are made about the size of the mountain, the amount the truck can carry as well as the speed in which the truck can travel from the mountain to its final destination.

First, a mountain can be thought of as a cone. To determine the volume of the mountain and the amount that must be transported I will assume that the size of an average mountain will be about 1 kilometer high or 1000 meters. Additionally, the radius of the mountain is a fourth of this number, so approximately 250 meters. Given these estimation, the volume of the cone is approximately 19,6250,000.

Secondly, we need to estimate how much volume the truck can cary. It is estimated that the truck is of average size. It wil estimated that the trucks carrying tray is a rectangle that is roughly 5×10 meters and 3 meteres deep. Given these estimation, the trucks volume is 150.

Based on the assumptions of the volume of both the average size mountain as well as the average sized truck, the truck will need to do approximately 1,308,333 trips from the mountain to the dumping site.

As the truck has to go back and fourth, carrying one load at a time it will have to travel a of 1,308,5000×10 miles x 2 or approximately 16,170,000 miles. However, when the truck is carrying a full load, it will travel at a slower rate in comparison to when it is going back to the mountain to pick up another load.

I will assume the average sized truck without carrying anything will travel at a speed of 60 miles per hour. Thus, return trips will cover roughly 1,308,000 miles, this will take the truck approximately 218 hours to complete.

However, a truck carrying the parts of the mountain will travel at a much slower rate. I will assume that with a load it will travel at a speed of approximately 40 miles per hour. Thus, trips from the mountain to the dump site will take approximately 327 hours to complete.

So given the problem to move an average sized mountain 10 miles and the assumptions made, it is estimated that it would take 545 hours to complete.

• Ethan Jun 16, 2013, 3:44 am

-average mt. 8,000 ft high
-assume mt. has square base, 10 miles each side, round miles to 5,000 ft
-8000ft x 5000ft x 5000ft= 200b cubic feat for the rectangular prism that contains this mountain
-200b/2= amount of year in the rectangle actually occupied by the mountain= 100b ft^3

Average truck has a 5ftx10ftx2ft bed= 100ft^3
100b/100= 1 billion loads of the truck to move the mountain

time per load: 45 minutes to load truck, 20 minutes to drive 10 miles (have to drive slow with full load,) 30 minutes to unload truck, 10 minutes to drive back= 105 minutes= 1.75 hours

1.75 hours x 1b loads= 1.75b hours
8,760 hours/ year- round to 10,000
1.75b hours/ 10,000hrs/yr= 175,000 years to move the mt

• jo Jun 18, 2013, 10:12 am

assume an average size truck has X meter cubic capacity, and the average mountain is approximately Y meter cubic volume, and can be deconstructed and reconstructed by the truck itself.

thus it would take Y/X passes to move the mountain.

let:
A be the time required for the truck to load a full truck load of the mountain materials.
B be the time required for the truck to unload and reconstruct the mountain materials.
C is the time required for the truck to climb the whole mountain.
D is the time required for the truck to move 10 miles.

then the time it would take to move the mountain 10 miles useing the truck is:
(Y/X)*(A+B+C+2D)

• h Jul 11, 2013, 4:25 am

A mountain of 10 Miles . 10 Miles taken to be diameter assuming the mountain is round at the base.

1 mile 5280 feet. 52,800 feet long mountain.
Radius = 52,800/2 = 26,400 feet

Area = 1/3 (pie * (26,400* 26,400 / H)

An average size truck dimensions are = 80 feet* 9 feet*12 feet (l*b*h)

one time area of mountain transported = 80*9*12 = 8640 cubic feet
Distance = x

Assuming = A truck takes 1 day to go to destination of relocation

Area transported in one day = As much volume is accumulated

No. of days =

at a time area

• Pavel Jul 11, 2013, 2:12 pm

Assume the average mountain of 3 000 meters high and 3 000 meters radius. The area size of such mountain is P=3.14*radius^2, it’s about 30 000 000 squarе meters. The cubic capacity is V=P*high*1/3, it’s about 30 000 000 000 cubic meters.

Assume the truck needs 1 hour to go to destination and come back. It works day and night. So the average truck can pick 30 cubic meters.

The result is that we need about 1 000 000 000 hours or 100 000 years to do this

• Prentiss Jul 15, 2013, 2:47 pm

Mountain size assm: 5000′ high, 5000 radius. Vol = 1/3 * pi *r *h. Mountain volume = 125,000,000 cf
Truck size : 8’x8’x25′. Vol = LxWxH = 1600 cf.
Truckloads = Mtn Vol/ Truck Vol = 80,000 loads

Cycle : load + drive + unload + return drive = 15 min + 20 + 5 + 10 = 50 mins/cycle
Duration = 80,0000 loads x 50 mins/load = 4,000,000 mins ~ 9 yrs

• Nick Pate Jul 20, 2013, 9:38 pm

I will assume that an average size mountain is about 1/4 of a mile high by 1/4 of a mile wide. To simplify, I will assume this mountain is a sphere. A mile is 5280 feet, so 1/4 of a mile is 1320. The volume of a sphere is (3.14 x d^3) / 6, so plugging my estimated average mountain into that equation, (3.14 x 1320^3) / 6 is about 230,000,000 sq ft. I will assume the average truck bed is 6x4x2 ft. With that assumption, the average truck can carry 48 sq ft of dirt. I will assume that each load will take 30 seconds to load into the bed of the truck and 30 seconds to unload. That means the actual loading and unloading will take about 4,800,000 minutes, which is 200,000 days or about 550 years. So, that’s just loading and unloading.

For the actual transportation, it takes 20 miles for the truck to drive to the depositing site and back. The truck will make about 4,800,000 of these trips, which is 96,000,000 miles of driving. Assuming the truck drives on average 30 mph, this will take 3,200,000 hours or about 350 years.

Adding the loading and unloading time with the driving time, it will take about 900 years for an average size truck to move an average size mountain 10 miles.

• CJ Jul 21, 2013, 11:56 pm

To estimate this question, I think we need to consider 5 factors:
1. Volume of an average mountain
2.Maximum volume that a truck can take
3.Driving speed to and from the 10 miles to dump the contents
4.Time it takes to upload the truck to full capacity
5.Time it takes to offload the truck contents

Starting from the first one. I would assume an average mountain is of the shape of a cone and thus has an average radius of 100 meters, a height of 1200 meters. Therefore, the volume of the mountain would be 1/3* pi * (100)^2*1200, i.e. 4*10^6*pi cubic meters.
2. Assume the container of an average truck is of 1 meter height, 4 meters long, and 2 meters wide. So, the volume of the container would be 1m*4m*2m=8 cubic meters.
3. Assume the driving speed to and from the dumping place is 20 miles/hour and thus the time it takes to and from the dumping place would be 2* (10/20)=1 hour
4. Time it takes to upload the mountain contents to the truck container. I assume there are two ppl using tools to haul the contents into the container and it takes them 3/4 hour to fill the container to full.
5. Assume it is much faster to offload the contents from the container to the dumping place, which takes only 1/4 hour.

Thus, overall time it takes to move an average mountain to 10 miles away would be (4*10^6*pi)/8*(1hour+3/4hour+1/4hour)=10^6*pi hours

• VR Jul 26, 2013, 6:02 am

5,500 days.

First off, lets consider that we need to move all the mountain volume using the trucks loading capcity (i.e. the trucks volume).
Lets then consider an average size mountain to be a pyramid with a base that is a sqaure.
Then, lets say that this mountain has each side of its base equal to the length of 50 avg. sized trucks lined up one after the other and a height of 100 avg. sized trucks stacked up vertically.

As for the avg. sized truck, let us say that it is a rectangle with length of 4 meteres, base of 2 meters, and height of 2 meters.

Thus, each side of the mountain is 200 meters long (50*4) and has a height of 400 meters (100*4)

As the volume of a pyramid is calculated as: V=1/3*(b^2)*h, and b=200 meters and h=400 meters, the volume of the mountain is approximately 5,300,000 meters^3

The volume of a rectangle is calculated as: V = b*l*h, and b=2 meters, l=4 meters, and h=2 meters, the volume of the truck is 16 meters^3

Thus, we will need apprxoamitely 330,000 truck loads (5,300,000/16) to move the entire mountain

That means that the trucks with have to make 330,000 round trips which means that it will travel 10 miles 660,000 times. That makes for total travel of 6,660,000 miles.

If the truck travels at 50 miles per hour, our travel time is 132,000 hours which is equal to 5,500 days

For this problem, the principal underlying assumptions are the following:
-100% of the voulume of the truck can be used to move the mountain
-the truck is countiounsly moving at 50 miles per hour
-upon arrival to the mountain, the truck is instantly loaded at 100% of its capacity
-upon arrival at destination, the truck is instantly unloaded and instantely being reconstructed.

• SY Jul 29, 2013, 7:46 am

How big is the mountain?

Having been to various mountains I would say that an average sized mountain is 2km in height and 4km in width. I will assume that the mountain takes a generic circular based cone shape. (i.e. radius is 2km)

Mass of mountain: (1/3)*pie*(radius^2)*height =~ (1/3)*3*4*2 = 8km^3 = 8,000,000,000 m^3

How much can the truck hold?

Assuming: length 6m; width/height 2.5m, the load of the truck for each journey is 6*2.5*2.5=37.5. Let’s round to 40 for simplicity.

Number of journeys required = 8bn/40 = 200 million

Time require = (# journeys)*(transport time + load time + unload time)

I assume an average speed of 40mph of truck (driving fully loaded at 30mph and returning unloaded at 50mph). Therefore transport time (to and fro) is 30min

Loading – I assume one can load the truck in 25 minutes. (at a rate =~ 1.5m^3/min)

Unloading – Much quicker because cargo is dropped out using hydraulic raisers and so unload time of 5 min.

Refueling – Ample time to do it when loading/unloading

Therefore, (in hours) Time required = 200m*(0.5+0.4+0.1)= 200 million

• Romain Jul 31, 2013, 7:50 am

Moutain height = 3000m
Mountain basis = 500m
Moutain volume = 176 625 000 m3

Truck volume = 8 x 3 x 2 = 48m3
Loading time = unloading time = transport time = 20 min

Number of trucks needed = 176 625 000 / 48 = 3 679 688
Time needed for a truck to load, transport, unload and come back = 80 min (1,3 hours)

Time needed = 3 670 688 x 1,3 = 4 771 894, 4 hours (or 198829 days or 544,7 years)

• Daniel Cong Aug 7, 2013, 2:09 pm

“Estimate how long it would take to move or relocate an average size mountain 10 miles using an average size truck”
An average mountain has a total amount of 1 million tons of earth. An average size truck can carry one ton of earth at once. It also takes 3 mins to load the truck and 1 mins to unload the truck. The truck drive at an average speed of 60 mile/hour which makes each round turn drive cost 20 mins. Therefore, for the truck to carry one ton of earth cost around 20+3+1 mins. So, to move an average mountain 10 miles, it takes about 24 million mins to do it

• ShawnTu Aug 13, 2013, 1:40 am

(1) Let’s first define the volume of averaged mountain:
Based on the experience, I am assuming the mountain occupies a square area (1 mile x 1 mile) and its height is 0.5 mile. To simplify the calculation, it appears as a cube. So the volume is: 1x1x0.5 = 0.5 mile^3 ~ 2 x 10^9 m^3.

(2) Now let’s consider the size of a averaged truck = 2x2x5 = 20 m^3

(3) Total number of transportations required: (2×10^9)/20 = 10^8 (times).

(4) In order to relocate, workers need time to mount the dirt, drive the car for 10 miles, and un-mount dirt. All these steps take time. Let’s assuming it takes 5 minutes to mount as well as unmount the dirt. And drivers drive at 30 miles/hr. so it takes 20 minutes total drive time for one way. Overall, a round trip costs 5 min (mount dirt) + 20 min (drive to relocation spot) + 5 min (unmount dirt) + 20 min (drive to mountain) = 50 minutes.

(5) Now assuming workers can work 12 hours a day to relocate the mountain. Number of transportation within the 12 hrs is 12 (hr) x 60 (minutes/hr) / 50 (minutes) = 14 rounds (with 20 minutes remaining).

(6) As a result, the total working days required to relocate the mountain would be (10^8) / 14 = 7142857 working days ~ 19569 years.

• zx Aug 14, 2013, 11:20 pm

Assume the average mountain is of a conical shape of 10km in base radius and 1km in height. That would give us the total volume of the mountain to be 1/3*pi*10km^2*1km=100km^3=1e11m^3. The average truck load volume can be estimated by 4m*2m*1m=8m^3, so it will take 1e11m^3/8m^3=1.25e10 runs for the truck to move the mountain away. Assume the truck drives at an average speed of 40mph, to make a round trip to and from 10 miles away would take half an hour. Therefore to move the entire mountain the total time would be 1.25e10*0.5hr=6.25e9 hrs. Each year has 365*24 hrs=8760 hrs. Hence 6.35e9 hrs equals approximately 7.1e5 years.

• sameer Aug 24, 2013, 11:34 am

Truck –
Capacity of the truck – 1000Kgs
Average time of the truck for one trip –
During Peak traffic – 2 hrs
During non-traffic time – 1 hr
Loading and unloading time total = 1 hr
Total time during Traffic for 1000Kgs – 3 hrs
Total Time during Non-traffic – 2 hrs
Assuming that the truck is refued while loading and unloading so no time is added for refueling
and the driver takes a break during the loading/unloading so no additional time there. The truck runs all the time till the process is completed

Mountain-
Weight of sand/gravel/other – 1000,000,000kgs

Road –
Peak time is there every 20 hrs- for every 3 hrs peak time there is 20 hrs non-peak traffic

No of trips = 1000,000,000/1000 = 1000,000
20hrs – 1000*10 = 10,000 kgs
3 hrs – 1000 kgs

23 hrs for 11000 kgs
how much for 1000,000,000 kgs
therefore 1000,000,000 * 23 /11000 = approx 2,090,000 hrs

• AO Aug 26, 2013, 2:05 pm

– 1) I assume that one average size mountain is 500m high, and 3000m * 3000m wide.
=> 3000*3000*500 = 4 500 000 000 m cube
Thus, one average size mountain is 4 500 000 000 m cube.

– 2) I assume 1 m cube of mountain weights 1500kg, or 1,5tons.
4 500 000 000* 1,5 = 6 750 000 000
Thus, one average size mountain weights 6 750 M tons .

– 3) I assume one average size truck can move 10 tonnes at once. Let’s figure out how many trips will be needed to move the whole mountain by dividing the weight of mountain by weight a truck can move at once: = 6 750M tons / 10 tons = 675M trips.
Thus, 675 M trips are needed to move the whole mountain.

– 4) I assume that a truck moves at 60km/hour (= 40mile/hour). (Please note that I am not taking into account the loading time in my calculations)
Thus, it take 15min for a truck to move 10 tonnes of mountain from its original location to a location 15km (10miles) further, then it take another 15minutes to go back to the original location, and get an extra 10 tons of mountain to move.
Thus the truck can move 20 tons / hour (= 2 trips/hour)
Let’s figure out how many hours are needed to move the whole mountain by dividing the total weight of the mountain by the number of trips per hour: 675 M/ 2 = 337 M hours
Thus, it would take 337 million hours to move the mountain.

337 M hours / 24 hours = 13,5 M days
Thus, it take 13,5 million days to move the mountain.

13,5 M days / 365 days = 38 000 years
Thus, it would take 38 000 years to move the mountain

• PS Sep 6, 2013, 5:00 am

25.000 YEARS

• link Sep 6, 2013, 5:23 pm

Assume the mountain is just dirt (as opposed to composition consisting partially of rock), so we don’t need to worry about blowing it up. Then since dirt is easily transferable by truck, the idea is to divide volume of mountain by volume of truck, to get number of trips required, then estimate time per trip.

I guess an average mountain is more like a large hill, so probably like the height of a tall building. Let’s estimate it as about 10 stories tall, so at 3 meters per story, we get the height of the mountain to be 30 meters.

Let’s approximate the average mountain to be conical, which has volume about half that of a cube. So volume is

(30 meters)^3 / 2 = 13 * 10^4 m^3

or approximately 10000 m^3.

A standard truck is on the order of 2 m in length, so about 10 m^3 volume.

So we need 1000 trips.

Round trip is 20 miles. With truck averaging 40 mph, this gives 30 minutes for round trip.

It probably doesn’t take too long to load/unload, so let’s say round trip + load/unload to be around 1 hour.

That gives 1000 hours.

Assume working day around 10 hours.

That gives 100 days, or a few months.

Setting up equipment takes order of days, so we were okay in ignoring that.

• Meeta Sep 15, 2013, 2:12 pm

11520000 minutes

• B.H. Sep 16, 2013, 12:07 pm

1) Total Time = (Time to break down the first mountain block) + N*(maximum time between transporting a block and breaking down a block)

where N is the total number of blocks the mountain is broken down into
Note that transporting a bock includes coming back to mountain site

Assumption: truck loading and unloading times are neglected

2) Estimate size of mountain
Let’s suppose the mountain is in the shape of a cone then it’s volume is given by
V=1/3 * pi * r^2 * h
if Mt Everest is about 8800 meters high, suppose the average mountain is about 60% as high,
then h=0.6*8800=5280 meters
Suppose also that the overall width of an average mountain is that of 2 football fields (100 meters length each)
then r = 100 meters

so V ~ 0.33*3.14*10000*5280 ~ 10300*5300 ~ 54,500,000 metercubed

3) Estimate N

Assume an average size truck is 7 meters long and 4 meters wide and 5 meters high
then the size of one block is 7*5*4=140 metercubed
then N=54,500,000/140 = 390,000
Assumption: the truck can support the weight of the mountain block

4) Estimate time to transport one piece

10 miles = 10 * 1600 meters = 16 000 meters
Suppose the truck travels at 30 Km/hr then
time to transport one piece = 2* 16000/30000 ~ 60 minutes

Suppose it takes 30 minutes to break a block of the mountain
Since 60>30,
then total time = 30 minutes + 390,000*60 minutes ~ 390,000 hours ~ 1500 days ~ 4 years and 1 month

• Shams Sep 20, 2013, 6:39 am

I took too long (30 minutes).
Assumptions:

Truck Volume:
3x3x5m = 45cubic meters

Time per trip: 20 minutes
Loading+Unloading = 8minutes (assuming conveyor belt system @ .1875cubic meter/sec)
Commute = 12 minutes (10mph average speed)

Mountain Assumptions:
– Pyramid Shape (square base)
– Average height 2km
– 35 degree gradient (means 10.84 x 10.84 sq km base)
– Volume= 78.34billion cubic meters

Mountain volume/ Truck Capacity = 1.74billion trips
1.74billion trips x 20 minutes = 34.82billion minutes = 24million days

• RB Sep 20, 2013, 1:45 pm

To estimate the time taken to move an average mountain over 10 miles in a an average truck we will need to firstly find out the following:

1) The volume of the mountain
2) The capacity of the truck
3) The speed of the truck in mountainous terrains
4) Time taken in loading and unloading

=> VOLUME
For this firstly I assume that
Height of the mountain= 2Km i.e. 2000mts
Radius: 1km i.e. 1000mts

So volume= pi*(radius)^2* Height* 1/3
= 2.094 cubic km
=
=> CAPACITY OF THE TRUCK
For the capacity of the truck we assume its a middle sized truck. So length= 5 mts; height= 2mts; width= 2mts
Capacity = 5mt*2mt*2mt = 20 cubic mts = 2*10^(-8) cubic km

So total number of trips = Approximately 10.5 crore = 105 million trips

3) Generally the speed of a truck can be taken around 70-80 kms per hour. But in mountainous terrain we can assume it to be say 50 km per hour

So total distance to be travelled = 10 miles * 2 (to and fro) for 105 million trips – 10 miles of the last trip
= 210 crore miles approx
= 335 crore kms

So travelling time = 6.7 crore hours

4) Time taken for loading and unloading

Assuming we have say 2 persons working towards this project. So the numbers of hours per loading (assuming they can load and unload with the help of machines) = 2hrs
Similarly time per unloading = 2hrs
So total loading+ unloading time per trip = 4 hrs
Total of all the trips = 42 crore hours

So total number of hours = 48.7 crore hours

But we have to add in this figure the following also
==> Time taken for filling petrol
Assuming capacity of the petrol tank of truck
100lts
Mileage = 10km/lt
So total number of times petrol needs to be filled = Distance to be traveled / (Mileage*Capacity of tank) = 33.5 lakh times
Assuming getting petrol tank full takes around 5 mins each time
So total time required to fill petrol = 2.8 lakh hours

THUS

Total time requires to transport the mountain 10 miles in our case = 48.728 crore hours = 2.03 lakh days = 55, 625 years approximately!

(We assume the work never stops and people work in shifts and also that the truck does not break down)

• Mars Sep 21, 2013, 12:01 pm

Average Mountain Size = 1,000 meter long * 100 meter wide * 100 meter high = 10,000,000 million cubic meter
5 meter long * 1 meter high * 3 meter wide = 15 cubic meter
Time taken to fill the truck once = 30 minutes
# of Trucks to be filled = 10,000,000 / 15 = 666,660 trucks
700,000 * 30 minutes = 350,000 hours
Traveling time 700,000 * 30 minutes per round trip = 210,000 minutes = 3,500 hours

Total Time Taken to move the mountain = Approximately 360,000 hours

• Guy Sep 23, 2013, 6:55 pm

First, I assume that all we’re doing here is moving the mountain from an inconvenient location to a more convenient one. That is, we’re not re-creating the mountain, as is, on a new site with the same material, we’re just scooping the mountain into a truck, driving 10 miles to the new site, dumping the truck and driving back.

Second, I’m assuming that we also have mechanized excavation equipment to remove the mountain and put it in the truck.

Third, I assume that we do not have to wait in order to cut any new roads needed to accomplish this project. That is, there’s a road to the top of the mountain, and any preparation of the loading site can be accomplished during the truck’s round trip.

We need to estimate a few things, which will involve some more assumptions.

How big is a typical mountain? Everest is 29,000+ feet tall, and 1000 feet is the minimum to be considered a mountain. Most mountains are in between. The oldest mountains in N. America are generally considered the Appalachians, and the tallest mountain on the E. Coast is Mt. Mitchell, which is around 12,000 (maybe 13,000) feet tall.

The Alps, Rockies, Andes and Urals are all newer, so MOST mountains are taller than the tallest Appalachian, but shorter than Everest. For ease of calculation, let’s assume an average mountain is around 15,000 feet, or approx. 3 miles. Again, for ease of calculation, let’s assume a cone shape and a radius of 2 miles at the base. The volume then is 1/3 * pi r^2 * h = 1/3 * 3.14 * 4mi * 3mi = ~12.5 cubic miles.

A typical Dump Truck is about 10 cubic yards. 1 cubic mile is over 4.5 BILLION cubic yards. So even if we have a 15 cubic yard truck, we will need over 30 million trips to move this mountain. 30 million minutes is over 57 years (30 mm / 60 / 24 / 365).

Without getting too complicated, since we now see the scope of the problem, if we assume it takes one hour round trip (load the truck, drive from old site to new site, dump the truck, drive back) and we never, ever have to stop for any reason, we are talking about 57 * 60, or 3,420 years.

• PHH Oct 3, 2013, 8:30 am

1,111,111 days 10 min

• Ashwath Oct 9, 2013, 1:21 pm

Volume of mountain (60 m radius, 80 m height) = 1/3*22/7*60*60*80=300,000 cubic meter
Truck volume = 2*4*6=48 cubic meter
On an average it takes the truck to travel up and down 10 miles is 1 hour
Loading and unloading 2 hours with a crane and JCB
Therefore in a working day of 9 hours 3 trips are possible
Therefore 300000/(48*3)=2100 days = 5.7 years

• ED Oct 17, 2013, 4:13 pm

In order to solve for how long it would take to move an average size mountain 10 miles using an average size truck, I would have to define an average sized mountain, based on my skiing experiences I can classify large mountains as 4,000 ft vertical based on Kicking Horse Resort and small “mountains” as 500 ft based on Blue Mountain Resort. I am assuming that there are equal amount large as small mountains based on the random fact that if the earth was shrunken down to the size of a cue ball it would actually be smoother than a cue ball – establishing relativistically the distrubution of large and small mountains to average out, resulting in the height of an average mountain as 2,250 ft. Assuming the mountain is conical, and that the city of Macchu Piccu was built near the top of a mountain and assuming that one could walk across Macchu Piccu in 4 hours at 3mph the diametre at the top of the mountain would be 12 miles. Therefore the diametre at the bottom, assuming a slope of 1:1 as the moutain wouldn’t be too tough to climb, nor too easy, would result in a diametre of 34,230 ft, a radius of 17,000 ft. The volume of the moutain is 1/3 * r(squared) * pie * height, assuming pie and 1/3 cancel each other out r2 equals 289M sqft multiplied by the height yields 650B cuft of mountain to move. To determine an average truck, I know that average trucks in Canada are limited to a length of 53′ height 12′ , width 8′. Assuming the cab length takes 4ft for engine, 4ft for bench, 4ft for sleeping/storage, and 1 ft for gap, that leaves ~40ft for storage, and assuming of the 12ft height, the wheels go up 2ft that leaves 10′ so the volume of an average truckload would be 40x10x8 = 3,200 cuft. Therefore moving the mountain would take 200M loads. To move a mountain 10 miles a truck has to drive 10 miles there and back, assuming on a highway at 65mph, therefore a truck can travel 20 miles in 0.3 hrs x 200M loads means it would take 60M hrs or 60,000 years.

• Getrude Oct 23, 2013, 5:59 am

30days

• ST Oct 23, 2013, 2:08 pm

250 yrs

• Nir Oct 30, 2013, 11:32 am

60 Years.

• Michael Nov 12, 2013, 4:03 pm

First we need to determine volume of the average mountain.

Lets assume that average mountain is 3 km tall and has a 20km diameter. and lets assume it is a pyramid rather than a conus for easier calculations.

So the volume will be 3*10*10/2*4=600 cubicle kilometeres

Lets assume that we are efficent and are extracting truck-size blocks from the mountain at the time when our track makes its journey so it does not consume additional time.

So now lets calculate how much time we need to transfer the mountain.

Let average truck volume be 10 cubicle meters.

So we need 600 bn/10 = 60 bn trucks to move the mountain.

let truck speed be 60 miles per hour and 5 minutes to load and unload and we get 0.5 hour for each trip.

Now 60 bn*0.5-3 bn hours. lets round it to 2.4 bn and divide by 24 to have days. we got 100 mm days now we divide it by 365 and we get around 250 000 years

• MS Nov 18, 2013, 2:19 pm

Assuming the average mtn volume was equivalent to 100k average trucks and each unloading roundtrip took 1 hr
it would take 100k round trips or 100k hours (assume 25hr/day, 4000 days or 12 years)

• vamshi Nov 22, 2013, 1:08 pm

it depends on speed of truck

• RE Nov 22, 2013, 6:40 pm

Assuming average mountain height is 2000 ft and for ease of calculation is one shaped like a rectangle of dimensions 2000 ft x 2000 ft x 1000 ft, the volume is 2000 ft*2000 ft* 1000 ft = 4e9 ft^3.

Assuming the truck is an average size passenger truck such as a Tundra, etc. equivalent, the cargo area is only filled to the top of the tailgate, and the cargo dimensions are 10 ft x 5 ft x 1 ft, the volume of 1 load is 10 ft x 5 ft x 1 ft = 50 ft^3.

Therefore, the number of loads would be 4e9 ft^3/50 ft^3 =
8e7.

Assume the truck can travel 60 mph each way (both to and from the mountain) and load/unloading time is negligible. 1 trip to take a load and return to the mountain would be 20 miles. For the last load, the truck would only travel 10 miles. Nonetheless, transporting each load would take 1/3 of an hour.

Therefore, 8e7 loads* 1/3 hr per load = 26,666,666.6 hrs With the last load only traveling one way, subtract 10 minutes, or 1/6 of an hour, giving 26,666,666.5 hrs.

• Francisco Nov 24, 2013, 5:21 pm

I approximate the volume of a mountain to that of a piramid. Which is 1/3 base multiplies the height.

I guesstimate that the average mountain is about 1000 metres high and has a base of 1000 metres x 1000 metres.

Total volume of the piramid is: 300 millios of cubir metres

Average track: I guesstimate 10 metres long, 5 metres wide and 3 metres hight. Volume: 150 cubic metres.

300million m*3 / 150 m*3= 2 million trucks needed or 2 million trips of the same truck.

I guesstimate that average speed of a truck transporting heavy stuff is 80km/ h. 10 miles are 16 km, that means the track takes 20 min to go and 20 min to come back, total 40 min.

40 minutes x 2 million= 80 millions of minutes

60 min x 24 hours= 1440 min. I round it to 1500.
1500 min x 7 days a week= 10500 min a week
In one month0 42000 min, I round it to 40000.

80Millions of minutes / 40000 = 2000 months= 166 years

• cm Nov 29, 2013, 11:56 am

0 days 0 hours 0 minutes.
The base of an average mountain spans over 10 miles because a mountain needs a large base to reach an average hight.

• Duke Dec 1, 2013, 3:05 pm

15,000 hours

• Ami Dec 4, 2013, 10:04 am

66,666 hrs

• Charrrr Dec 5, 2013, 2:31 am

I assume the mountain as a cone. Assuming the height and radius to be 2000mtrs and 500mtrs respectively the total volume of the mountain stands at 50,00,00,000 cubic meters.

Now I calculate the volume of the truck used as having dimensions 10x5x5=250 cubic meters

So it would take the truck 20,00,000 rounds to get the truck load to the new site 10 miles away.

Assuming that the truck takes 20 mins to load and 10 mins to unload at the new site. That makes the loading-unloading time of 30mins per trip.

Now if the truck travels with an average of 100 miles/hour. The truck should take 6 mins to get to the new location.

So the total time taken for the mountain rubble to be transportated is 30+6=36 minutes.

Since this trip is to be repeated 20,00,000 times so total time taken in minutes = 7,20,00,000 minutes

That comes down to 4166.6667 years. I wonder if that is a logical answer though.

This is the first estimation question that I have attempted. Your reviews on how well I did it are awaited.

#Note for Mr. Cheng- I dont know if i should be saying this since you are too experienced and seasoned in what you are doing here. You are doing an excellent job at guiding us beautifully on how to go about the case interviews and otherwise too. Your insights are a real help.#aspiring consultant.

• ML Dec 5, 2013, 9:43 am

Problem: how long will it take to move an average size mountain 10 miles using an average sized truck?

first reflection – that seem like a far from practical approach…

Overall Method: Time = distance/speed (hours)
Speed – estimate speed (average speed for fully loaded truck and empty truck) (km/hours)
Total distance – estimate no. of times truck would need to move total volume (km)
Total volume – estimate (m3)
Total time = distance x 2 x (tot mountain volume/truck volume) / average speed (hours)
Calculation = 16*2*(2 500 000 /160) / 50 => appr 10 000 hours
realistically: assuming working 8 hours/day, 5 days/week and 50 weeks per year => 4,5 years – my answer
Note, we don’t have very big mountains or many weeks of vacation where I come from 😉

• FS Dec 6, 2013, 3:13 pm

Assumption: Mountain is cone-shaped
Height = 3000 m
Diameter = 1000 m

volume of mountain = (1/3)*pi*r^2*h = pi*500*500*1000 = 25*pi MM cu. m

1 truck container = 10m * 2m * 2m = 40 cu. m

Number of trips required = (25*pi MM / 40) = 2 MM (appx)

Distance = 2*10 MM mi
avg speed = 30 mi/h
Continuous time = 20 MM/30 = 80 years (appx)

Fuel Tank = 100 L
Mileage = 10 mi/L
Therefore refuel after 1000 mi
Therefore number of fillups = 20 MM/1000 = 20K
Refill time = 10 min/refill
Total refill time = 200 K min = 4 months (appx)

Total movement time = 80 years – 4 months = 79 years and 8 months.

• Celina Dec 7, 2013, 3:10 pm

96 hrs

• MA Dec 11, 2013, 4:28 pm

100,000,000 minutes or 1,666,666.67 hours

• rfts Dec 14, 2013, 5:43 am

1.5 years

• Emiliano Dec 29, 2013, 6:43 am

I assume the mountain is a cone:
– radius = 1,5 km
– height = 3 km
–> Volume = approximately 7 km^3 (7.000.000 m^3)

I assume the truck’s trailer measures as follows:
– length: 10 m
– width: 4 m
– height: 4 m
–> Volume of the truck’s trailer is 160 m^3

I assume the truck travels at an average speed of 50 miles/hour, which means it takes 2 minutes to drive 10 miles, therefore a total of 4 minutes to drive back and forth from the old to the new site. At this speed, the truck will need:
# trips = 7.000.000/160 = 43.750 to move the whole mountain

At 4 minutes each it gives 175.000 minutes which means:
– 2.917 hours
– 122 days
– 4 months

I also assumed the truck works 24 hours per day, 7 days a week.

Bests

• navratn Dec 31, 2013, 4:32 am

2000 years

• Aniruddha Deshkar Jan 1, 2014, 5:06 am

if have an area where height is 25 meters and length is 18 meters and width 1 meters how many H frames required of 2 X 1 meters

• Kirill Feb 26, 2014, 10:00 am

225

• Temir Jan 4, 2014, 3:03 am

1. Size of an average mountain. 500 meters X 500 meters X 200 meters = 250,000 X 200 = 50,000,000 m3.
2. How much m3 can a truck carry. Regular cars are four meters long. Truck is 3 regular cars long = 12 meters. Front part is 2 meters, so the back side is 10 meters long, width 3 meters. Height of the back side is 3 meters tall. So the amount of soil it can carry is 10 meters X 3 meters X 3 meters = 60 m3.
3. Depending on the road quality, 10 miles of driving with 50 miles/hour back and forth may take 20 minutes (for the sake of simplicity). Time to put and take out soil may take 10 minutes. In total we will spend 30 minutes per one round.
4. Lets assume that truck works 10 hours a day. So it will carry 10 hours / 0,5 hours X 60 m3 = 1200 m3 per day.
5. It will take 50,000,000 m3 / 1200 m3 = 4,200,000 days. If we work 300 days per year, then it will be 4,200,000 days / 300 days = 15,000 years.

The answer is 15,000 years

• Kirill Feb 26, 2014, 10:04 am

I would take a half of the first step, because mountains are usually have a pyramid shape and pyramid equals to half of a cube.

• iyar May 11, 2014, 8:36 am

they actually equal one third of a cube..

• Jason Jan 4, 2014, 10:26 pm

a truck of height 2ft, length 20ft and breadth 5 feet has an area of 200 cubic feet. Similarly a mountain of height 2000ft and radius of 1000 ft would had an area of 1b cubic feet. Hence it will take almost 5 million trips to move the mountain.
Assuming loading unloading and to and fro travel time to be an hour, it will take 5 million hours to transport.

• John Jan 5, 2014, 5:38 pm

Assume that average size of a mountain is 1km*1km*500m/3 = 0.17km3
= 170,000,000m3, and the capacity of a truck is 2m*2m*3m = 12m3,
the average velocity of the truck is 50km/hour, and it takes 6 minutes (0.1 hour) to load or unload stuff. So for a round trip, it takes (16/50＋0.1)*2 = 0.85hours, and there are totally 170,000,000/12 = 14,000,000 rounds, so , 14,000,000* 0.85 hours = 12,000,000 hours, which is 500,000 days, or about 140 years. But the truck does not work without rests. So assume it works 8 hours per day. so we triple the outcome and get the outcome of 420 years.

• Chad Jan 9, 2014, 2:26 am

Mountains are cone shaped, so the volume of a cone is pi*r^2*h. they are usually wider than they are high. h=300 ft r=500 ft so the volume of the mountain is 3*2500*300. 3.14 round down to three (point finger down). 3*300 is 900, bump it to 1000 for good simplicity (hand flat). 1000*2500= 2,500,000 ft cubed. the size of the mountain.

A truck bed is about 6x4x2 or 48 ft cubed, round up to 50 ft cubed. how many trips would it take to do 5,000,000 ft cubed, and divide that in half. 5 mil divided by 50 is 100k, so it would take 50k trips. how long does each trip take?

Assuming the mountain is a easily shovel-able pile of dirt (no demolition), it would take 10 minutes to completely load/unload the truck, 20 minutes total. driving 60 miles per hour for 20 miles (there and back), it would take 20 minutes. 20 + 20 = 40.

50,000 trips at 40 minutes each. 2 million minutes. then convert this into days. 60×24 is 240+1200=1440 minutes in a day. round up 1500 minutes in a day (point down bc fewer days included). 2 mil divided by 1500. It goes into 1000 times to get 1.5 million. Now how many times does it go into half a mil? 100×1500 is 150,000, three times (300) gets 450,000 (low again). So it takes 1,300 days. 365 days in a year. 1,300 divided by 365. Round up to 380. 380 +380 = 760 + 380 = 1140 + 380 = 1520. Above 300 (up again, so neutral).

About 4 years.

• Chad Jan 9, 2014, 2:30 am

divide 4 years by 3 because I messed up in my very first formula, it is one third the side of the cylinder I calculated.. so 1 year and 4 months if it moves it continuously.

• cheuk Jan 11, 2014, 3:56 am

2600years

• Mehdi Boudoukhane Jan 11, 2014, 10:44 am

4,000 years.

My reasoning:

Total time = (Size of Montain / Size Truck) * 10 miles / speed Truck.

I have no idea what could be the average size of a montain. I know Mont Blanc is about 5,000m high. According to that, I assume that the height of an average montain is 1/5 of the height of Mont Blanc, i.e. 1 km. The assumptions being anyway very rough, I assume a cubic shape for the montain => 1 km^3.

For the truck, I assume a size of 2 m x 2 m x 5 m = 20 m^3.

For the average speed of a truck, I assume 60 miles per hour. Since there is also the time of loading and unloading, I divide this number by 3 and I end up with a speed of 20 miles per hour.

Replacing these numbers in the above formula, I get 25 million hours, which gives about 1 million days. Assuming 250 working days per year, my final answer is 4,000 years

• EK Jan 12, 2014, 11:23 am

13100 days

• Nitasha Jan 12, 2014, 1:05 pm

To tackle this question we need to look at:

1. volume of an average mountain
2. volume of an average truck
3. speed of that truck
4. time taken to load a truck

We know that Mt. Everest is about 8000m in height. Let us assume, on average, a mountain is 5000m tall. Assuming a pyramidal structure, let’s assume a base diameter of 4000m. This means that the volume of an average mountain is 1/3*pi*(2000)^2*5000 = 20 billion cubic meters (higher end)

Let’s assume that the average dump truck has dimensions of 10m*5m*5m giving us a volume of 250 cubic meteres

An average truck would require to make 20,000,000,000/250 = 80 million trips to the mountain and back.

Total distance travelled= 80,000,000*32,000m (or 4 miles, 2 miles*2)=2560 billion m = 2560 million km

Let’s assume the truck moves at a pace of 80km/hour
Therefore time taken to make all the trips= 32 million hours

Additionally, let’s assume it takes 30 mins to load a truck = 40 million hours spent loading the truck

Total hours= 72 million hours = 3 million days = 833 years (approx)

• Matt Jan 14, 2014, 4:07 pm

Average mountain: 1km*1km*1km = 1km^3 volume
Average truck: 5m*2m*2m = 20 m^3
Return trips: 1km^3/20m^3 = 5*10^7
Truck speed when empty: 100 mph
Trip time when empty: 10 miles/100mph = 6 mins
Truck speed when full: 50mph
Trip time when full: 12 mins
Total trip time: 18 mins
Load truck time: 22 mins
Unload time: 20 mins
Total time for one trip: 1h
Total time: 50 million h ~ 5000 years

• Francesco Bosi Jan 17, 2014, 12:23 pm

I would assume:
average mountain height: 900m
average mountain base diameter: 8km
Noting that a mountain resembles a cone I would apply the formula: V= 3,14 x r x h/3 and obtain a total volume of 3768 m3.
I would then estimate the truck capacity. Assuming that an average truck has a 7m long, 3m tall and 3m wide loading space, the total capacity of the truck is 63 m3.
It is now time to divide the volume of the mountain by the truck capacity to estimate how many 10 miles long trips will take the truck to move the mountain; the result is 3768/63= 60 ( rounded number, the exact result is 59.8).
Assuming an aveage speed of 20mph it takes the truck 1h for each round trip; this means 60 hrs driving.
To this number we have to add loading/ unloading time. I assumed a loading time of 1h and a 30mins unloading time (1,5hrs per truck load in total). Multiplying this number by 60 truckloads we obtain 90hrs in total.
My final estimation is therefore 60 +90 = 150

Francesco

• Francesco Bosi Jan 17, 2014, 12:29 pm

OOps, silly mistake. The mountain volume is 3678000 m3; it takes the truck 60000 trips = 60000 hrs + 90000 hrs of loading/unloading operations. Total time required: 150000 hrs = 411 years.

• OUSMAEL Jan 21, 2014, 3:55 am

10 MILES DIVIDED BY THE SPPED OF THE TRUCK

• SG Jan 21, 2014, 12:40 pm

2,017 days, 8 hours, 20 mins

• MG Jan 29, 2014, 11:06 am

To find out the answer, we need to estimate the volume of an average mountain and the volume of space available in an average truck and the speed at which the truck can travel back and forth between the two locations. Plus we also need to know the loading and unloading time of the truck.

Time required would be no of time the truck would have to load, go the new destination, unload and comeback multiplied by time taken for each cycle.

Time taken = no. of cycles * time per cycle

now time per cycle = Load time + unload time + time taken in going to the destination + time taken in returning back

these day machines are available which can quickly load/unload a truck. I thinks it will take maybe 10 seconds for each.

Also distance is 10 miles. truck would be slow when travelling with full load as compared to when empty. An empty truck can move at say 50 miles an hour whereas a loaded truck may move at say 30 miles an hour.

therefore time taken in round trip would be (10/50 + 10/30) hrs.

so out cycle time is (10 sec + (10/50 + 10/30) hrs)

now no. of cycles would be volume of mountain/volume of space in truck.

mount Everest is 8 km high. so I would take an average mountain to be half of that say 4 km. Also a mountain can be taken as a cone having apex angle of 45 degrees.

therefore the volume of mountain would be (using the formula to calculate volume of a cone) = (1/3)*pi*r*r*h = (1/3)*3.14*2*2*4 = 16 km cube (approx)

now volume of an average truck. I can assume the average truck to be a cube with a side of about say 20 ft or 6 meters.

therefore volume of truck is 6*6*6 metre cube = 216 metre cube

therefore no of cycle required is (16*1000000)/216 = 80000 approx.

so time required = (10 sec + (10/50 + 10/30) hrs) * 80000

((32*60+10)/3600)*80000 hrs

(800/36)*( 1930) = 40000 hrs (approx)

• MZ Feb 2, 2014, 7:15 pm

2*10^11 hours

• b Feb 4, 2014, 11:20 am

90days

• Florian Feb 5, 2014, 10:47 am

My truck would need 3000 years.

• Nikita Feb 6, 2014, 10:09 am

100 years probably for my truck

• Jeffrey Feb 10, 2014, 8:48 am

How many boulders with 1500 kgs can sustain by 18 cubic dumprtuck?

• Christian Feb 11, 2014, 10:31 pm

1/3 (B^2) * H = Area of triangular prism.

If the mountain were 2,000 feet tall, ~1 mile per side wide (5,000 ft), (~16,666,666,666 cubic feet), and a pickup truck’s bed is 5x6x2 (60 cubic feet), then it would take ~277,777,777 trips.

Driving 60 miles per hour, it would take 12 minutes per round trip (with no stops).

277,777,777*12 minutes = 3,333,333,333 minutes / 60 min per hr / 24 hr per day = 2,314,814 days, or 6,341 years.

• RCT Feb 17, 2014, 10:51 am

My truck would take 5k years

• Qingdi Feb 18, 2014, 8:20 am

1.5 million years

• Zhu Feb 18, 2014, 8:47 am

average mountain: 1 km height with 1 km radius bottom and it is cone like. So the volume: pi*r*r*h*1/3 = 3.14 * 1000 * 1000 * 1000 *0.33 = 1.04 * 10 (9) m(3)

Mountain made of rocks: rocks consist major with silicon dioxide (major component of sands, sands are small pieces of rocks). The density of silicon dioxide is around 2.5 t/m(3)

So the total mess is around 2.5 * 1.04 * 10 (9) = 2.6 * 10 (9) t

The decomposition of the mountain do not need a long time ( several years maybe) as we have so powerful dynamites. Thus, the time needed in this case is omitted.

A normal truck in China ( I am a Chinese) can hold 4t of cargo.

So it will take the truck around 6.5 * 10 (8) times go-and-back journeys. Which means the truck need to load and unload for this much times and the total miles covered during the journey is around 1.3 * 10 (10) miles.

To load 4 t of rocks onto a truck, if you have a right lifting machine, it will take around 15 min. For unloading, you just need to pour out all the rocks, so will take only 5 min at most.

The truck carrying rocks cannot drive so fast (for safety), I set its speed at 40 miles/h (which is a quite high speed for a truck with cargo in China). Then the return journal will take 30 min.

Therefore, each journal will take around 50 min.

Then the total time we need is
6.5 * 10 (8) * 5/6 = 5.4 * 10 (8) hrs
= 2.25 * 10 (7) days = 6.2 * 10 (4) years

So I will probably need 62,000 years.

Lastly, one truck can never do this job as it cannot last so long.

• Prosenjit Sen Feb 23, 2014, 12:52 am

Average Mountain – 1000 tonnes of earth and stone
Capacity of a Truck is – 20 Tonnes carrying capacity
Distance to move – 5 miles
Truck Speed when fully loaded 20 mph
Time to Load/Unload to full capacity 3 hours
Total Trips in a Day 2 mountain moved in a day 40 Tonnes
Time required – 1000/40= 25 days

• Prosenjit Sen Feb 23, 2014, 12:52 am

Average Mountain – 1000 tonnes of earth and stone
Capacity of a Truck is – 20 Tonnes carrying capacity
Distance to move – 5 miles
Truck Speed when fully loaded 20 mph
Time to Load/Unload to full capacity 3 hours
Total Trips in a Day 2 mountain moved in a day 40 Tonnes
Time required – 1000/40= 25 days

• Tung Mar 2, 2014, 6:43 pm

Total time = Time traveling with garbage + time traveling without garbage.
Time traveling with garbage = Number of time traveling x time per travel = Mountain volume/ truck volume x (travel time + dumping time).
Mountain volume = 1/3 x pi x r^2 * h
Average mountain –> h = 1000m, r = 50m (assumption)
pi is rounded down to 3, so:
Mountain volume = 50^2 x 1000 = 2,500,000 m3
Average truck has a 2 x 3 x 4 load, so the volume is 24 m3 which is rounded up to 25
The average travel velocity is 20 mile/hour, so 10 miles mean 0.5 hour.
Dumping time is 6 minute, which mean 0.1 hour
Time traveling with garbage = 2,500,000/25 x (0.5 + 0.1)
Similarly, time traveling without garbage = 2,500,000/25 x 0.5.
So total time is 2,500,000/25 x 1.1 = 100, 000 x 1.1 = 100, 000 + 10,000 = 110,000 (hours) = approximately 4400 days

• Parul Garg Mar 7, 2014, 2:41 am

An average size mountain would be 3.5 km in height(I am estimating this on the basis that the highest mountain Everest is 8 km high). In terms of diameter, I would say approximately 12km, so radius is 6 km. Assuming a cone shaped mountain, the volume would be 1/3×22/7x(6000m)^3x3500m=appox 800×10^12m^3. Assuming density of 10kg/meter cube, since water has a density of 1kg/meter cube, the weight would be 800×10^13 kg. Assuming an average truck has a capacity of 1 tonne, i.e. 1000 kg, the truck would have to make 800×10^10 trips. If it has be relocated across 100 km, and travels at a speed of 20km/hour while going and 50km/hour while coming back empty, the journey would take approx 7 hours, it would take 5600×10^10 hours. which is approx 80 billion months, assuming approx 700 hours in a month and 21 billion years, considering there are 12 months a year.

• Trang N. Mar 13, 2014, 2:25 pm

It possibly takes 3240 estimated hours to move an average sized mountain 10 miles using an average truck.

• pranav Mar 15, 2014, 1:43 pm

volume of mountain = 4/3 pi (10000)^3
volume of truck = 3*2*2
no. of trucks required = (10^12)/3
digging speed = 10 trucks per hour
digging time = (10^11)/3
filling time = (10^10)*2/3
truck speed = 60mph
total transportation time = 10*2/3*(10^10)
therefore total time = 10.67*(10^10)

• Lulu Mar 20, 2014, 2:42 pm

We need to estimate the average size of a mountain and the average capacity of a truck. The truck size is relatively easy to guess. Let’s say 5m*3m*2m=30m^3. The height of a mountain ranges from a few hundred meters to 8848 meters. Let’s simply assume that it’s 1000 meters high and it’s a perfect cone shape with the diameter of the base as 1000 meters. The total volume of the mountain is then 1/3*PI*(1000 m)^3 ~ 1*10^9 m^3. Assume the speed limit for the truck is 40 mile/h, then a round trip takes 20/40 h=0.5 h. Neglect the time for loading/unloading, the total time needed would be 1*10^9/30*0.5 ~ 2*10^7 h, or ~ 2000 years.

• Jeffrey Wong Mar 22, 2014, 6:02 am

Assuming average size of mountain (in Pyramid shape)
= (length x breath x height) /3 = (1000 x 1000 x 1000)m / 3
= 333,333,333 cubic meter
= 333,333,333 tonne (assuming 1 cubic meter = 1 tonne)

Assuming average truck load is 200 tonne
=> it will require (333,333,333 ton/200 ton) = 1,666,667 trucks loads to shift the mountain.

Assuming it takes 10mins to fill up the truck;
Assuming average truck speed is 10 mins to travel 10 miles
=> will take about 20 mins for the round trip
Therefore, it will take 30 mins to fill the 200 tonne truck, drive to dump 10 miles away and return for another load.

HENCE, it will require 1,666,667 trucks loads x 3omins or 0.5hr
=833,334 hr = 34,722 days = 95 years if using 1 truck; 9.5 yrs if using 10 trucks; and about 1 yr (11.5 mths) if using 100 trucks.

• rafei Mar 28, 2014, 8:13 am

70 minutes total time trip ( 5 to charge 30 min to go , 5 decharge and 30 min come back )

1 truc is 0,01% Total quatity of dust in a mountain

therefore 70 min * 10 000

Which give us : 1 year 121 days

• Lasse Mar 31, 2014, 3:31 pm

Let’s say a average a average mountain is 2500m high and 5000m in diameter. With h*r*Pi/3 this makes roughly 5.25 million tons, when one ton equals one m³.
Our average truck can load 20 tons, this means the driver needs 2.5 millions loads. With 20miles to go for each trip and an average speed of at least 50mls/h, this would make roughly 25mins per trip.
To sum this up, it would take 5.25 million minutes, 90000 hours, 3600 days or roughly 10 years (including some holidays).

• Moe Apr 20, 2014, 9:05 am

50,000 years

• Alexey Nikityuk Apr 22, 2014, 3:32 am

I would start from calculating this mountain volume in m3.

The formula is V=1/3*S*H. Lets assume H=1000m high and the base looks like a big not ideal circle. Circle square equals A=Pr^2 with r=2500m and P=3.14

So our formula equals V=1/3*(3.14*2500*2500)*1000. Roughly estimate will be 6.3B cbm.

Then lets estimate volume of average truck. Assume it has standard box-like space for load with 2m height, 3m lenght, and 2m width which gives us H*L*W = 12cbm as volume of average truck.

Lets calculate number of trucks needed to move the mountain. For that we divide 6.3B by 12 which gives us roughly 525M of trucks.

Distance of 10 miles equals 18 km=18000 m. Avg speed for truck is 50 km/h leads us to 22 min one way per truck.

There is also time for loading the truck. Assume it takes another 10 mins for loading it and 8 mins to unloading, 18 totals.

As given we have 1 truck, means it needs to go one way full, and empty back so we need multiply 525M by 2 = 1B trips for 1 truck.

So in the end we calculate 1B trips*(22+10+8)=1B trips*0.67 hour = 670M hours for 1 truck => => roughly 70.000 years

• Alex Kushner Apr 24, 2014, 11:11 pm

To gauge the size of a mountain, I compare it when looking at it as a background to my house. It needs to be much bigger than my house (not a hill). So suppose the ground floor of my house is 3,000 square feet.

It takes roughly 100 of my houses to span the diameter of the mountain (from one side to the other). For sake of the calculation, assume the mountain is relatively spherical after adjustments are made for its irregularities. Therefore it is 300,000 ft diameter.

Calculating then the volume of the mountain, using 0.5*(pi)*(radius)^2, where radius in this case = 150,000. The volume of the mountain is 11,250,000,000 ft^3.

Then consider the average size moving truck. Call it 20 ft x 10 ft x 10 ft = 2,000 ft^3.

Dividing these two values, it takes approximately 5,625,000 trucks to move the mountain. Carrying a full truck, we cannot exceed 20 miles per hour for fear of tipping over, starting and stopping, each round trip takes one hour, plus 30 minutes per loading period. (one load + one unload)

That is 5,625,000 hours of loading/unloading and 5,625,000 hours of driving = 11,250,000 hours.

• Dhawal Apr 27, 2014, 10:59 am

8 * 10^8 days.

• Michael Apr 27, 2014, 11:30 pm

Assuming a mountain that is 10000 feet tall and 6000 feet in diameter, and assuming a standard sized truck that can move a volume of dirt that is 4 feet by 4 feet by 8 feet, I have estimated that it would take 366, 555,762 hours to move this mountain 10 miles.

• Ashish Gupta Apr 30, 2014, 2:52 pm

Assuming that the average height of a mountain is 6,000 ft, and the base has a diameter of the same 6,000 ft, the square area of the base is appx 28M sq ft and the volume is appx 85B cu ft, or appx 3B cu. yds of dirt/rocks.

Each truck can hold 30 cu. yds of material. Therefore, 100M truckloads of material must be moved. If it takes 1 hour to load the truck, drive it 10 miles, unload the truck and return, then it would take 100M hours to move the mountain. At 24hrs/day and 365 days/yr, this works out to appx 11,000 years.

• ganesh Apr 30, 2014, 5:01 pm

assume pyramid shape
ht 2000m, base 3000m X 3000m
volume of pyramid = 2000 x 3000 x 3000/3 = 6 x 10 power 9 m3
TRUCK
truck bed size = 4m x 2m x 0.5m = 4m3
speed = 60mph
time to go with load= 10mts
time to come back empty = 10mts
time to load = 40mts
So, 1 trip per hour
operating hrs = 12, so 12 trips/day
NUMBER of trips = 1.5 x 10power9
NUMBER of days required = 1.25 * 10power8
truck operation = 365 days per year
number of years = 1.25 x 10power8/365
estimating ( rough calculation) = 3.33 x 10power5 years

• Célia May 2, 2014, 10:31 am

– Calulate the volume of the mountain : to simplify, let’s say the mountain has a pyramid shape with 100meters each side and a height of 50meters. Volume = 100 x 100 x 50 = 500 000 m3
– Estimate the volume of the truck : 10m x 2m x 2m = 40m 3, let’s say 50m3
=> Number of going back and forth = 50000
– Estimate the time for loading and unloading the truck and the transport time.
=> Volume of bucket of the mechanical digger = 1m3
=> Time of loading = #bucket x filling time and buckett movement = 50 x 1min = 50 min to fill the truck
=> Loading time = no need for bucket so 5 min to empty the truck.
=> Transport time = truck’s speed is approximately 50km/h at full and 60km/h for an empty truck (mountains roads…) so for 10km it will be 12min for the way to go and 10min to come back.
-> 1 cycle time = loading time + Transport time to go + unloading time + transport time to come back.
-> 1 cycle time = 50 + 12 + 5 + 10 = 77 about 80 min.
Total time = #cycles x cycle time = 50 x 80 = 4000 minutes = 70h
With 7h work per day the result can be achieve in 10 work days.

• Alex May 5, 2014, 11:21 am

Mountain > Proxy for the overall truck load to be carried over ten miles > Pyramid on a quadratic ground with height h = 2,000 m and and side lengt l 0.25 x 2,000m = 250 m > 500,000 m^3 truck load

Truck > Volume it can carry > 3.5 m x 2 m x 1.5 m = 10.5 m^3

Numbers to Mountain and Truck result in 48,000 truck loadings that are necessary for the Mountain to be moved

Assumptions on speed of the truck over the 10 miles (fully loaded = 45 miles/hr and empty = 50 miles/hr) loading times on the mountain and the spot 10 miles away (1/2 hr and 1/4 hr respectively) result in time needed per one full transport step > 1.2 hrs

Result: 48,000 loadings x 1.2 hrs = 57,600 hrs

• DM May 14, 2014, 5:34 pm

93 000 years

• MH May 17, 2014, 7:24 am

600 million hours

• Anuj May 19, 2014, 1:53 am

Assumptions:-
1.Let’s say an averagse size of a truck is 10*12 = 120 m2
2.Let say the average size of the mountain is = 7200m2
3.The truck travels 8 hrs a day
4. The speed of the truck is 36 km/h as it is on mountain range
5. 1 mil = 1000m
The distance travelled = 10 miles
The number of times the truck would have to take a part of the mountain = 7200/120 = 60
The speed of the truck is 10 m/s
Distance = Speed * time
10*1000 = 10*t
t= 1000h
8hrs – 1 day
1000hrs – 125 days
Now the whole mounatin will be moved in 60*125 = 7500 days.

• Sauarbh May 19, 2014, 7:27 am

Assuming mountain to be in a shape of an quilateral pyramid of each edge of 40m.so we need to shift around 9000m^3 volume.Assuming each truck would be able to shift 5 meter cube at a time and assuming truck travelling with a speed such that it takes half an hour to go to and fro.Hence it would take 900 hours.37 days 12 hours

• RB May 24, 2014, 1:30 pm

If we take the mass of an average mountain to be about 2 million tons. And assume that the average truck can carry about 20 tons of material, it would take about a 100,000 trips. If each trip 10 mile trip @ 60 mph took 10 minutes, all trips together would take ~17000 hours or ~708 days.

• Arjan May 28, 2014, 3:11 am

so lets think,
define average mountain to be 4.5 km high
volume of piramid shaped mountain is 80 percent of a cube say 4.5 km squared is 16.2 km3
weight of mountain is at 2.5 ton/m3 is approx 40 billion tons
approx truck load is 40 tons
so you need one billion truck loads
say one truck can deliver 10 loads a day at 10 miles distance
if you use 100 trucks, they can together deliver 1000 loads a day , you ll need one million days
thats 2700 years.

• Joy May 29, 2014, 10:19 pm

let’s say the height of an average mountain is 10,000 feet, and to make it simple, its bottom is a circle which occupies 30,000 square feet, the volume of a cone equals 1/3*S*h=1/3*10,000*30,000=100,000,000=100 million cubic feet
an average truck can carry 500 cubic feet per time. It takes 10 minutes to load and 10 minutes to unload each round. It takes roughly 10 minutes for the truck to travel 10 miles one way. So to finish a full round: load + travel + unload + travel back = 10+10+10+10=40 minutes

100 million/500 = 200,000 rounds
200,000*40 minutes = 8,000,000
8,000,000/(60*24) = 8 million/1,440 = 5,500 days

• JW Jun 11, 2014, 12:44 pm

Asumme that the truck has the capacity of carrying 10m^2 of earth, and an average mountain has a volume 600 times more than the truck so say 6000m^2. Thus, in order to move the mountain, the truck will need to transport the earth 600 times. Since there is only one truck and its average speed is 30 miles/hr, 10 miles of travelling will take 20 minutes. Also because there is only one truck, it needs to go back and fourth. 600 * 20 = 12,000 minutes, but because the truck has to travel back, we multiply the result by 2, this will be 2,400 minutes in total. 24,000/60 = 400 hours = 16 days

• Abhishek Navlakha Jun 12, 2014, 8:20 am

Assumptions:
1. Avg Mountain size = 1000 tons
2. Avg Truck size = 20 tons
3. Sp approximately 1000/20 visits are needed to move the complete mountain i.e. 50 visits.

Now we calculate time for each visit.
Load time to move the gravel to truck (Vol = 20 tons).
Assume 0.5 ton is lifted and put in truck in 1 minutes. So for 20 tons you will need 40 minutes

For simplicity assume avg truck speed on the road from start to end is 40 miles / hour. To cover 10 miles one way the truck will need 15 minutes. Assuming unloading requires 1/4th time of loading, the unloading time = 10 minutes. (0.25 x 40 minutes). Assume returning speed is same and hence duration is same. So for one visit the time required for the truck is 40 + 15 + 10 + 15 = 80 minutes.

Since we said that 50 visits will be needed, the total time needed to move the mountain is 80 x (time for 1 visit) = 80 x 50 = 4000 minutes.

If we assume a working day is 8 hours (and lunch is 1 hour) there are 7 productive hours in a day.Hence, in a day truck can make 4 complete visits. To completely move the mountain the truck will need approximately 50/4 i.e. 12.5 days which is 12 days and 6 hours.

Further to be more accurate, the mathematical time needed will be 4000 /420 = 9.5 days. So it should take anywhere between 9.5 and 12.5 days if we assume that the workers are 100% productive during those 7 hours.

• Lucas Jun 12, 2014, 10:52 am

We need to calculate the amount of time required to relocate a mountain (of avg size) 10 miles away using an avg truck.
Let’s assume that our goal is to calculate and express the time in number of years.
Having said that,
T: time.
T: (numers of required trips) x (speed of each trip).
Speed of each trip: how long does it takes to an avg truck to cover, once it is full charged, a distance of 10 miles?
Let’s assume the avg speed to be: 60 miles per hour.
It means that to cover 10 miles, our avg truck will take app. 10 minutes.
Now, focus on the number of required trips (nrt): this depends upon 2 variables,. indeed:
NTP: (AVG Mountain Size)/(AVG truck charge capacity).
So, we need to calculate the avg mountain size.
Let’s check what we know:
First, let’s assume that to be classified as a mountain, one peak should not be lower than 1.000 meters.
Meanwhile, the highest peak in the world is app. 8.000 meters.
We can asssume that on average, a mountain tend to be around 2.000 meters.
We need to calculate the lenght and how large it is, on average.
Let’s assume as a proxy the avg population of each mountain village in europe…we finally arrive to consider:
base: 5 km, h: 2km, l: 1km, avg volume: 10 km^3.
Now, focus on a truck: in europe there are different standard.
We can assume an average as one of those to drive which you do not need a special driver license.
According to existing rules, we know that this size, in volume is:
lenght: 4 mts. high: 2 mts. large: 1 mts.
So we have a 8 cubic meters of volume (chargeable).

Now, we need to calculate the ratio between the avg mountain size and the average volume of charge:
number of trips required: 1.250.000 (avg mountain volume/avg chargeable volume per avg truck).
So:
Duration: 1.250.000 trip x 10 mins/trip: 12.500.000 mins.
1h: 60 mins. So: 208.333 hours.
1 day: 24 hours, so: 8.680 days.
Number of working days per year: 220.
Number of years required to relocate the avg mountain with an avg truck: 39.45.
Are u sure u want to be stuck in this bizi?
Thanks for your precious help!
Luca

• Lera Jun 24, 2014, 10:10 am

8 years

• Melissa Jun 26, 2014, 9:09 am

Suppose an average sized mountain weighs 2000 ton, and an average sized truck can carry 5 ton. Also suppose it takes one day to move a part of the mountain onto the truck (a process involving shoveling), but once the part is on the truck it should take a negligible amount of time to transport 10 miles. So 2000/5*1=400 days

• JS Jun 26, 2014, 11:18 am

39 days of continuous work

• gb Jul 5, 2014, 1:57 pm

60 days of continuous work

• ALVARO DEL PORTILLO Jul 7, 2014, 2:08 pm

340 years

• Chris Jul 7, 2014, 4:55 pm

“Estimate how long it would take to move or relocate an average size mountain 10 miles using an average size truck”

Assuming that the truck being used to move the mountain can carry about 50 cubic feet of material in a given trip and moving at around 50 miles per hour makes each roundtrip approximately 40 minutes + an additional 20 minutes for loading/unloading and the and the mountain itself is around 200000 cubic feet large then it would take approximately 40000 trips for the truck to fully move the contents of the mountain. 40000*1 hour for each roundtrip equals 40000 hours total to move the mountain. 40000/24 = 1666 days to move the mountain

• Mike Jul 14, 2014, 1:42 pm

Estimate how long it would take to move or relocate an average size mountain 10 miles using an average size truck.

1. The avg dump truck bed is 8′ x 3.5′ x 20′ which equals a volume of 560 cubic ft. It is never filled exactly to the rim, so let’s use 500 CF for estimating.
2. The mountain is 5000′ high and 5000′ across at the base and roughly cone shaped for a volume of 32724923475 CF
3. The truck travels good roads at highway speeds and loading/unloading is done in the same time each load- Estimated time per round trip: 5 min load/get on the road/ 10 min travel time at 60mph/ 5 min unload/start back/ 10 min travel time back to reload= 30 min trip time.
4. Taking these numbers: 32724923475CF/500CF/trip= 65449847 trips to move the volume of the mountain
5. 65449847 trips x 30min(.5 hr)/trip = 32724923.5 hours
6. 24 hours/day, so the number of days working 24 hrs/day would be: 1363538.5 approx. and with 365 days in a year, it would take approx. 3735.7 years.
7. IF we estimate this based on a workday of 10 hrs/day x 5 days/week, the number of years goes even higher: 12587 years rounded up- a job for your family forever!

• QT Jul 15, 2014, 6:29 am

17 years.
We need to estimate three things: volume of all the rocks, debris, etc that make up the mountain, the volume of material that an average truck can contain, and the time it takes to load, drive 10 miles from the mountain to the dumping site and back, and to unload.
1. Volume of the mountain: an average mountain has a base and a peak, roughly the same geometry as a cone. let’s assume the average height is 1,000m (i’m from Vietnam and the highest mountain here is over 3,000m. so take into account high and short mountains, even hills, 1,000m seems reasonable) and the radius 100m. so volume is 100^2*1000*Pi (3.14, let’s make it 3) =30 million cube meters
2. Volume of an average truck: i’m not talking US-sized trucks which are bigger than the ones I usually see at construction sites that are dotting the map of Hanoi. the ones I see are about 20-25 meters long, 3 meters tall and 8-10 meters wide. For length, i subtract the 5 meters at the front used for cabins where drivers sit, so the length of the containing area is 20 meters. 3 meters tall, take out 1 meter (for tires). that leaves 2 meters. Volume of an average truck, then, is 20*2*10=400 cubic meters
3. So we will need to use this same truck: 30 million/400 = 75000 times over to move this mountain. Now let’s estimate the time. The truck has to load, drives 10 miles with rocks on it to the dumping site, unload, then drives 10 miles back empty before loading again. I call that 1 cycle. How much time is in a cycle?
4. Assume there’s only 1 crane and it is continuously scooping rocks into the truck. From scooping to dumping and back, it’s about 5 minutes. How many scoops? Well, the part of the crane that does the scooping (excuse my lack of vocab) is similar to an upside down cone, with the radius at the base and its height roughly 2meters (i’m 173 cms tall and from the look of it, I can easily fit in that scoop). Therefore, each scoop is about 2^2*2* pi = 24 cubic meters. A truck’s volume is 400 (calculated above) => 400/24 = 15 scoops * 5 minutes each = 75 minutes to load that truck.
5. The distance is 10 miles. I assume the driver travels at 60mph (quite fast for a truck load of rocks, but time is money), so 10 miles to and from will take 20 minutes. Unloading takes another 10. So from loading to unloading, it’s 75+20+10=105 minutes. Take into account of minor malfunction or disturbance on the road, let’s call it 2 hours. We have to use the truck 75,000 times over -> 150,000 hours/24/365 = 17 years.

• sekoo Jul 26, 2014, 8:37 pm

1- Average size of a mountain
2-Average capacity of a truck
3- Round trip duration
4- Load / Off-Load duration
5- Number of hours worked / day
6- Maintenance duration of the truck
7- Gasoline fulfillment

1- Avg. Size of a Mountain
-Assuming the mountain is Pyramid shaped
w= 500 Mt
l=500 Mt
h=1000 Mt

Total Volume= (500*500*1000)/3–> ~100 Mn cubic meter

2- Avg Capacity of a Truck

l= 10 mt
w= 3 Mt
h=2 Mt

Capacity = 60 but taken as 50 cubic meter

3- Two different trip times

– Loaded trip speed = 30 Miles /hr –> It takes 20 Min.
– Empty trip speed = 60 Miles /hr –> It takes 10 Min.
Total 30 Min.

4- Loading= 25 minutes, Offloading: 5 minutes
Total: 30 Minutes

Total Operation Time: 1 hour for each time

5- Assuming truck is operating 15 hours / day
6- Assuming using the same truck (without having it getting scrapped).Maintenance will be required in every 3000 hours worked.

If it operates 15 Hours / day this makes ~2 maintenance per year. In each maintenance if we assume the truck will be out of service for 2.5 days, it will be operational for 360 Days / year

7- Gasoline fulfilling is assumed to be handled during out of service hours. It will be disregarded

The truck will make 15 times loading and offloading / day
15 times * 360 = 5400 times / year

Each time it can carry 50 cubic meter. 100 Mn cubic meter requires 2 Mn times of loading and offloading operation

2Mn over 5400 times / year = ~370 years.

• RM Jul 28, 2014, 11:20 am

Let us assume that the mountain moves at 1 mile per hour when the truck is at full throttle, then it would take 10 hours to reach 10 miles and so on.

• p.c. Jul 29, 2014, 6:14 am

Estimate how long it would take to move or relocate an average size mountain 10 miles using an average size truck.

***
Facts/Assumptions
***
Mass of mountain: 100 b kg
Capacity of truck: 10 k kg
Distance: 10 mi
Loading time: 1 hr
Unloading time: 1 hr
Transit speed: 20 mph
Workday length = 9 hours
# Days worked per year = 333 (workers get holidays and some Sundays off)

***
Calculations
***
Transit time:
Distance / speed
10 mi / 20 mph = 1/2 hr

Time per cycle:
Loading + Transit there + Unloading + Transit back
1 hr + 1/2 hr + 1 hr + 1/2 hr = 3 hr

Cycles per day:
Day length / cycle time
9 hrs / 3 hrs = 3 cycles per day

Mountain moved per day:
Capacity of truck * cycles per day
10 k kg * 3 = 30 k kg

Number of days needed:
Mass of mountain / amount moved per day
10 b kg / 30 k kg = 1,000,000/3 = 333,333 days

Number of years needed:
333,333 days / 333 days ~ 1,000 years

• SL Jul 31, 2014, 9:52 am

1. Volume of an average mountain

2000m high
1000m square base
Volume = 2000 x 1000 x 1000 = 2bn / 3 = c.700 million cubic metres

2. Volume of an average sized truck ‘trailer’

8m x 2m x 2m = 32 m3 ; say 30 cubic metres

3. Number of truckloads of mountain that need to be moved

= Moutain volume / tuck volume
700,000,000 / 30 = c.23 million visits

4. How long will each visit take?
4 parts to each visit:

a) load the truck with a JCB or similar
(Assume someone else is breaking up the mountain while the driver is driving back and forth) = 10 minutes

b) Drive 11 miles (1 for the mountain – 2km = c. 1 mile + 10 for the trip) – say 30 mph = 22 minutes

c) Dump the contents of the truck at the new site = 3 minutes (assume tipper truck)

d) Drive back to original mountain = 22 mins (assume lighter truck does not drive appreciably faster)

Total time for 1 visit = 57 mins, say 1 hour

5. Total time to move the mountain = time for 1 visit x number of necessary visits

1 hour x 23 million visits = 23 million hours
Round up to 24 million hours and you have 1 million days for one person working at 24 hours a day (plus whoever is breaking up the mountain)
Working at 8 hours a day you have 3 million days
Working 8 hours a day for 300 days a year you have 10,000 years
On this timescale, how much of a factor will erosion be…? Plus mortality…

• Adam Aug 6, 2014, 9:13 am

4 days, 8 hours

• P Aug 6, 2014, 7:53 pm

1,000,000

• Audri Aug 7, 2014, 10:45 pm

I know absolutely nothing about the size of mountains, but here is my logic:

The average construction truck size is about 7ft by 8ft and 6ft in depth, so it has a capability of carrying 336 sq ft. For these purposes I will round it to 350sq ft (assume some overflow).

The mountain is much harder to estimate, but they are fairly tall formations for their relative width, so it must be at least twice as tall as it is wide. The mountain I will move will be 4,000ft x 10,000ft for a total of 40 million sq ft.

The actual moving process requires several assumptions, including the labor to load and unload the mountain, potential truck break-downs, and whether this truck is working at night and holidays. For the purposes of this question, these are my assumptions:

2 persons loading/unloading truck
16 hours/day (2 worker shifts)
300 days/year (which will accommodate for truck maintenance as well as Sundays and big holidays)

If the truck moves quite fast (60mph) it will take 20 minutes round trip. However, the loading and unloading time will take quite a bit of time as well. The use of a crane will speed this process up, so that if done efficiently could be done in an average of 15 minutes at each location (unloading is a faster process than loading). This means that a round trip will take 50 minutes. Or, 19 trips a day. 5700 trips a year. This is 1,995,000 a year, or rounded up, 2 million sq ft a year.

It will take 20 years to move a 40mil sq ft mountain.

• LA Aug 20, 2014, 8:29 pm

1,000 hours

• H C Aug 23, 2014, 7:15 pm

800 hours

• Ayrat Sep 5, 2014, 1:55 pm

lets assume that average mountain has a dimensions of 200 m * 200 m * 1000 m*. Truck can handle 5 m* 2m* 2m. Time to load truck on average might take 1h, for simplicity. and to move to 10 miles 0.5 h. So 400 000 m3/ 20 m3 = 20 000 times to load truck. So 20 000 times * 1h is 20 000 hours spend to load 1truck. and 20 000 * 0.5 = 10 000 hours to transport. 30 000 hours to move mountain to 10 miles. Around 1 000 days, or 3 years

• Sandro Sep 11, 2014, 10:05 am

I’m trying to find the number of tourists in Florence each year.
How would you estimate the number of hotel in a city?

• Villard Sep 16, 2014, 5:52 am

13 000 years

• Van Sep 16, 2014, 11:21 am

First of all, we need to define how big is an average mountain and an average truck
Secondly, what kind of mountain we are talking about, there are mountain with lot of soil or mountain with tree or without tree, mountain with coal. Because different kind of mountain takes very different time to move.
Thirdly, what is the meaning of move here, it mean move to another place with the same size or we just need to move all the thing in the mountain and put them everywhere without the shape of a mountain as long as it is 10 mile from the old place.
Let’s assume that the mountain weight 600 tons of normal soil without tree and the average truck can carry one tons. For 10 miles it take the truck 1 hour to move and come back the the old place to carry. So for one day, working 8 hours, it can take 8 tons. So it need : 600/8 days to do it. Assume that we do not need to make the shape of the mountain.

• XQ Sep 17, 2014, 12:36 am

100billion hours

• Isabelle Sep 23, 2014, 4:23 am

“Estimate how long it would take to move or relocate an average size mountain 10 miles using an average size truck”

10 miles = Around 15 km.

Factors correlated:
– The size of ‘average size truck’
– The size of the mountain
– The average time needed to fill up the truck
– The average time needed to travel back and forth from point A to B
– The average time needed to unload the truck

**Assuming that the truck does not need to be re-fueled along the way and the workers do not need to rest.

My basic formula:
1. Time needed = (How many times the truck need to go back and forth) x (Time to reload + Travel time x 2 {back & forth} + Time to unload)

2. How many times the truck need to go back and forth = (Size of mountain) / (Size of truck)

—–
Now we need to answer the question 2 first before proceeding with question 1.
Size of average mountain: I’m not a mountain expert but lets estimate 5,000 m x 5,000 m (height, width). Since the mountain is a shape of cone lets assume that its around 2/3 of 25,000 m (volume if the shape is cube) – which means about 8,000m-cube
Size of truck = 2 m x 4 m x 2 m= 16m-cube

So,
How many times the truck need to go back and forth = (Size of mountain) / (Size of truck)
= 8,000 m-cube / 16m-cube = 500 times.

Now we move on to Question 1. First we need to figure out the answers for sub-questions.
1. Time to reload: Assuming the truck is equipped with automatic fork, it may take 5 minutes to reload the truck.
2. Travel time: The distance is 15 km. Assuming there’s no traffic and the truck run for 75 km/h, travel time is 0.2h or 12 minute one way, or 24 minute return (Lets assume its 25 minute for return journey).
3. Time to unload: 5 minutes, same as time to reload.

Now, as we have gathered our data, we can calculate our estimate:
Time needed = (How many times the truck need to go back and forth) x (Time to reload + Travel time x 2 {back & forth} + Time to unload)

Time needed = (500 times) x (5 + 25 + 5)
Time needed = 500 x (45)
Time needed = 22,500 minute = 22,500/60 = 375 hours = Approximately 16 days.

Answer: Based on my estimate, it would take approximately 16 days to move the mountain.

• David Sep 24, 2014, 4:31 pm

Factors correlating wiht how long it would take to move or relocate an average size mountain 10 miles using an average size truck?

1. The average time it takes a truck to move 10 miles
2. How much an average size truck can hold
3. The size of an average mountain

Time to move an average size mountain = average time it takes a truck to move 10 miles x 2 (for the truck to move back and forth between the mountain and the destination) x (size of an average mountain/size that an average size truck can hold)

average time it takes a truck to move 10 miles (assume the truck is running at an avg of 60 mph for those 10 miles) = 60 mph/10 miles= 10 minutes

size of an average mountain = size of an average rock x 100 million rocks
= 1 square foot /rock x 100 million rocks = 100 million Square feet

size an average truck can hold = 8 feet x 10 feet x 10 feet = 800 square feet

Time to move an average size mountain = 10 minutes x 2 x (100 million square feet/800 square feet)

Time to move an average size mountain = 20 minutes x (100 million square feet/800 square feet)

Time to move an average size mountain = 20 minutes x 12.5 million square feet

Time to move an average size mountain = 20 minutes x 2.5 million + 20 minutes x 10 million

Time to move an average size mountain = 50 million minutes + 200 million minutes = 250 million minutes

300 million minutes / 60 = 50 million hours /25 = 2 million days

• ElmerGS Sep 24, 2014, 10:17 pm

lets say max height of mountain is 8km (everest) and minimun 0. Lets assume more smaller mountains so average mountain should be around 3 km height. Assume also a cone with angle 45° so radius equals height. If pi=3 then volume of cone is (3km)^3=27E27 m^3

Now to the volume of typical truck. lets say it is .5mx1.5mx3m (hxwxd) = 2.25 m^3.

Now lets say it moves at 50 miles per hour in average per trip (30 charged and 70 uncharged) which means 20 miles takes about 25min.

Then the rate is 2.25m^3/25min~.1 m^3/min

Therefore, Time=Volume/Rate=27E27/1E-1=27E28 minutes.

Which is about 5E27 hours = 2E26 days =5E23 years

• JIAN Sep 26, 2014, 8:40 am

Assumed Background:
Let’s say the mountain is 10,000,000 tons; the truck can load 10 tons at max load, its speed with empty load is 60 miles per hour; with full load, it will 30 miles per hour; to put the truck full load needs 1 hour, dump from full load to empty needs 30 minutes, the tank of the truck allow the truck travel 100 miles without refill, refill tank from empty to full needs 10 minutes. Also the working time is 8 hours per day and 5 days per week and there is only one truck will be used to do the moving.
Assume the truck starts work with full tank of gas.

Analyzing:
round travel time = empty travel time + full load travel time
move time per unit = round travel time + load time + dump time
total moving distance = (mountain size / per moving size) * 20 miles
total gas refill count = total moving distance / 100 miles
total gas refill time = total gas refill count * 1/6 hours
total time =( (mountain size / move time per unit + total gas refill time) / working hours per week ) / 52

Result will be:
10/60 +10/30 = 10 minutes + 20 minutes = 0.5 hour
O.5 + 1 + 0.5 = 2 hour
( 10,000,000 / 10 ) * 20 = 20,000,000 miles
20,000,000 / 100 = 20,000 times
20,000 / 10 = 2,000 minutes / 60 = 33 hours
total time = ( ( 10,000,000 / 2 + 33) / 40) / 52 = 2,403 years and 10 months

• Shuqun Oct 8, 2014, 11:27 am

total time = #journeys * (time to load the truck + journey time + unload time + journey time)
#journeys = mountain size / truck container size
mountain size = volume of a circular cone = pi * 10^2 *100 *0.5 = 15000 m^3
truck container size = car size = 4*2*1.5 = 12 m^3 =15 (roundup)
#journeys = 15000/15 =1000
time to load truck = (container size / loading tool size) * (time to fill loading tool and unload) = (15/1) * 10 sec = 150 sec =3 min
journey time = 15 min (assume 40miles/hr)
As loading time is 3 min, guess unloading time is 1 min
total time = 1000 *(3+15+1+15) = 34000 = 3000 min = 50 hrs

• Daniel Oct 8, 2014, 4:29 pm

Step 1: Let’s approximate the mountain shape with a cone. Let’s assume that an average size mountain is a cone that is 1 km high and that has a base with a 3 km radius. Its volume is equal 1/3*pi*r*r*h =1/3*pi*3*3*1=3*pi, or approx. 10 cubic km (10 bn cubic m).
Step 2: Let’s assume that an average truck has a base 3*5 meters and when loaded the substance takes a shape of a pyramid that is 1 meter high. The volume of this pyramid equals 1/3 of height*base, which is 1/3*5*3*1=5 cubic meters.

Step 3: The truck will be able to relocate the mountain in 10/5=2 bn runs.

Step 4: Let’s assume that an average truck speed is 45 km/h. Let’s take that 10 miles equal 15 km (instead of 16 for the computational convenience). Hence the traveling time of a truck (one way) is 1/3 of an hour. Two ways will take 2/3 of an hour.
Let’s also assume that loading of a truck takes 30 minutes since it involves digging the ground and unloading only 10 minutes since the substance can be just thrown down from the truck.
Altogether loading and unloading take 40 minutes which is 2/3 of an hour.
The time total is 2/3+2/3=4/3 of an hour per one run.
Step 5: 2 bn runs will take 2bn*(4/3)hours=8/3 bn or approximately 3 bn hours.
Answer: 3 bn hours (under the taken assumptions)

• Douglas C. Oct 13, 2014, 7:22 pm

1. Size of the truck = 10 ft x 40 ft = 400 sqft
2. Size of the mountain = 4000 ft x 1000 ft = 4M sqft / 2 = 2M sqft
3. Truckload = 50,000 truckloads
4. Load time = 5 minutes x 2 = 10 minutes
5. Travel time = 10 minutes x 2 = 20 minutes
6. 30 min per load = 0.5 hours per load
7. 25,000 hours
8. 2000 hours per shift per year @ 3 shifts …roughly 4 years
Not accounting for maintenance, repair and gas stops. Maybe close to 5 years.

• natalie Oct 15, 2014, 5:39 am

100 miles is around 160km, given 100km/h, one cycle will be just short of 4 hrs, if load and dump time are included.

depending on the type of material of the mountain, we will assume it is consisting of a good solid manganese/iron ore which is quite heavy, around 100tons with an average size truck per cycle.
The mountain of average size, i compare with half the size of Table mountain (South Africa), should be around 500million tons, this depends heavily what your framework of an average size mountain is.
given that, 1million cycles ends up to be 4million hours, continuous operating (hot-seat change over) and with a 80% maintenance availability, million hours.
now what is 5 million hours in terms of days or months, it will take you 570 years minimum with one truck.
given that this most of the times are expected from mining companies all over the world, one can understand why they choose to invest billions of dollars into mega size equipment.
so economically scaled!

• CW Oct 30, 2014, 7:27 pm

Estimated answer is 22 days.

• Jon Nov 24, 2014, 2:09 pm

I approximated the mountain as a cone with the formula of pi*r^2*h/3 which I approximated to r^2*h. I assumed the average hight of a mountain is 800 meter and the radius to 500 meters. With that in mind, the volume of the mountain is 2 million m^3.

Assuming the standard truck have a loading space of 2*2*4 m^3 this create a need for approximatly 100 k rounds.

Assuming one round takes 1 h and 10 minutes (20 minutes to drive and 25*2 minutes to load) this will take about 100 00 hours. Here I assume that the mountain is worked on so that the driver can just load the parts.

one day is 24 hours which I round to 25 and one year consists of about 250 workdays, we get 100 k/25 = 4000. 4000/250 = 16.

Hence, my answer to this is 16 Years.

• Evan Dec 8, 2014, 5:37 pm

The solution to this problem requires, the travel time and the number of trips required.
My first step was to establish a value for the volume of mountain. I used the equation for volume of a cone, this was in my opinion the best was to estimate the shape and size of an average mountain. I used a height of 6,000 ft (a value close to mountains near my hometown) and a radius of 5,000 ft (given mountains near me are fairly steep) to get an estimate of 150 billion cubic feet of mountain.
Next I assigned values of what an average truck bed volume would be. I used 4x7x10, a value I believe accounts for an average truck, bigger than an everyday pick up but smaller than a dump truck, and rounded up to 300 cubic ft.
Using the two volumes I calculated the required number of trips to be 500 million.
The next step was to establish a trip time. Given an average speed of 40 mph the 10 mile trip would take 15 minutes. Additionally it would take some time to load/unload the truck, I believe the load would take longer so I estimated 50 minutes for load and 35 to unload. This yields a total travel time of 100 minutes.
Finally multiplying total trips by total time, It would take approximately 50 billion minutes to move the average sized mountain 10 miles.

• Marcelo Dec 11, 2014, 11:14 am

time = # of travels * time of each travel
# of travels :
– the truck has 2 * 3 * 10 m3 of volume = 60 m3
– the mountain has a height of 4.000m and a base diameter of 4.000m. So it has a volume of 250.000.000m3.

time of each travel:
– average of 30 miles per hour
– so it is 20 minutes for going, 20 minutes for goind back and I considered 20 minutes for filling the truck. So it’s 1 hour per travel.

Finally, the time is 1 hour * 250.000.000 of travels, which is equal to 250.000.000 hours, or aproximately 10.000.000 days or 30.000 years.

• GC Dec 15, 2014, 2:04 pm

To answer the question, I will try to estimate:
1) the mass of the mountain,
2) the overall time it will take an average truck to load, unload and drive 20 miles,
3) the load a truck could carry,
in order to estimate the time it will take to move the mountain 10 miles away.
To simplify my calculations I will use meters instead of miles and kg instead of lb.

Knowing that the world’s highest mountain, Mount Everest, rises over 8000 meters, I hypothesize that an average mountain’s height would be at 1000 meters and its base at around 2000 meters. I further assume that the shape of the mountain resembles a cone; inconsistencies around the shape are canceled out.

The volume of such a mountain is given by the formula (3.14)*(r^2)*(height/3). Since r and h are large numbers 3.14 is cancelled out with 3 and V=1,000,000,000 m^3.
Assuming that mountains avg density is 2, the mountain’s mass should be 2,000,000,000 kg (density=mass/volume).

Let’s assume that an avg truck can carry up to 5 tons that means it will take 400,000 truck rides to move the mountain, also assuming the volume of each load fits within the truck.

With an avg speed of 40 miles/hour it will take 15 min for the truck to complete half a ride and 30 mins for the whole ride (I use avg speed because the truck will return faster without the load). Adding 10 min to load and 5 to unload that means 45min in total for a truck to move 5 tons 10 miles away and get back.

Time to move the mountain 10 miles away= number of rides needed * minutes / ride= 400,000 rides * 45 min/ride= 18,000,000 min. Divided by 60 that is 300,000 hours. Divided by 24 this is 12,500 days. Divided by 365 that’s is approximate 34 yrs – assuming my calculations are correct.

Two things could change this result: 1) the truck’s speed, but I cannot argue that if the truck goes up to 70ml/hr that will change the result significantly 2) the load the truck could carry. Either one truck with double the size or an additional truck could take that time down to half.

• Ilya Dec 15, 2014, 4:53 pm

My answer, based on assumptions and calculation listed below is 2,559.8 hours.

Assumptions:
– The average mountain may be considered a mountain having average height of (maximum mountain in the world, which is approx. 8 km) and (lowest mountain in the world, which is 0 meters), which gives us a 4 km height
– The volume of the mountain for the simplicity may be calculated as volume of the cube, which gives us a 64 sq. km
– For simplicity reasons the 1000 ton weight of the mountain may be considered equal to 1 sq. km
– Average truck capacity may calculated as average of (maximum truck capacity, which is let’s say 40 tons) and minimum truck capacity (let’s say 0 tons) which gives us a 20 tons average truck capacity
– The mountain is located outside of the city (as most of mountains do), thus the country speed limits may be settled as in many countries, i.e. 90 km/h outside of the city
– Average full truck speed on the 10 miles road may be considered as 60 km/h maximum (given the time for reach this speed on this 10 miles road), average empty truck speed is 80 km/h
– Loading time may be considered as 15 min, unloading – 5 min (let’s suggest the truck has own mechanism for fast unload)
– The truck starts directly from the mountain
– All the arrangements to the reallocation are at hand (i.e. all the technics which will load the mountain mass into truck is at place, all the personnel is ready to work)

Based on these assumptions the average time of reallocating the mountain on a 10 miles distance may be calculated in the following way:
1) Number of tons in the mountain = 64,000 tons (i.e. 64 sq. km * 1000 tons per 1 sq. km);
2) Number of trucks required to reallocate the mountain = 3,200 trucks (i.e. 64,000 tons / 20 tons);
3) Delivering of first truck of mountain to the 10 miles destination = 0,6 hours (i.e. 16 km (which is 10 miles) / 60 km/h + 15 min (load time) + 5 min (unload time))
4) Number of rides left = 3,199 (i.e. 3,200 trucks – 1 truck);
5) Delivery of each next 20 tons will take 0.8 hours (i.e. time for road back of 16 km (which is 10 miles) / 80 km/h + 0.6 (which is the same as time for delivering of first truck))
6) Time required for delivery of rest mountain = 2,559.2 hours (i.e. 3,199 trucks left * 0,8 hours)
7) Total time required for delivery of mountain = 2,559.8 hours (i.e. 0.6 hours (first time delivery) + 2,559.2 hours (time required for delivery of rest of mountain))

• LK Dec 30, 2014, 2:26 am

Considering a mountain of radius 1 km and height 2 kms. Volume will be around 2 cu. kms
Truck volume will be around 24 cu metres. the truck takes around 30mins to transfer and return.
Calculating it gives 35 years.

• AR Dec 30, 2014, 5:22 pm

800,000 minutes:

answer = (mountain volume / truck volume) x round trip time

mountain volume: 800 m x 200 m = 160,000 m^2
truck volume: 4 m x 2 m = 8 m^2
round trip time: 30 mph -> 10 miles = 20 minutes each way x 2 = 40 minutes

(160,000 / 8) x 40 = 20,000 x 40 = 800,000 minutes

• pratyush Jan 3, 2015, 12:07 pm

27 Days 6 Hours 20 minutes.

• Karl Jan 6, 2015, 7:41 am

Lets assume average size mountain weights around 20 000 tonnes and Average truck can take 2 tonnes at once. Therefore truck needs to do 10 000 trips with the ‘mountain’ and 10 000 trips back- therefore 20 000 trips needs to be done.
Truck going with speed of 60 miles/h can do 3 full (there and back) 20 miles trips. If we assume one loading takes a 20 minutes – its 2 trips per hour.
Therefore for 20 000 trips needed to move the mountain – truck needs 10 000 hours. Assuming truck can work 10h/ day its 1 000 days.

• Jun Sung Jeong Jan 16, 2015, 10:11 pm

I went about solving the case with the following logic…

The first step I took was to identify the key activities that would consume time and then, segment those activities respectively. The three key activities I noted were…

1. Travel time between location A (original location) to location B (new location)
2. Time to “on-load” mountain
3. Time to “off-load” mountain

Thus, our answer is going to be contingent upon the following equation…
Total time = travel time + “on-load” time + “off-load” time

Assumptions I made were…
1. Only the trunk of the truck was a viable source of transport. I also assumed that the soil must be filled only within the rectangular cube space of the trunk (since soil might be flying out of the truck if filled like a cone, and hence, the failure to transport the mountain)
2. Mountain most represents a cone, and if fitted within a cube, the cone would fill approximately 50% of the volume.
3. Truck is travelling at a relatively “safe speed” at 40mph

Analyzing the Case…
1. To figure out the total travel time on the road, I had to first calculate the volume of both mountain as well as the truck. To simplify my life, I assumed that the length, width, and height of the trunk space was 5 by 5 by 4 feet, which gives us a cubic ft volume of 100 ft cubed. Now, I turned my attention to the “conish” mountain. Again, to simplify our lives, I made some assumptions that the mountain’s length, width, and height was 2000 by 1000 by 5000 ft, which gives us a cubic ft volume of 10,000,000,000 ft cubed; however, I have previously made the assumption that cone would fill 50% of the cube. Thus, the actual volume would be 5,000,000,000 ft cubed. Dividing the mountain’s volume by truck’s volume gives us 50,000,000 units. Now, at a speed of 40mph, the truck can travel from location A to location B in 30 minutes, or .5 hours, or a round trip in 1 hour. We now multiply 50,000,000 units by 1 hour, which gives us a total travel time of 50,000,000 hours.

2. The next branch to analyze is the time to “on-load” the trunk of the truck. However, I recognized that the time to “on-load” the trunk would be different at different intervals. To explain myself, digging up dirt from the top of the mountain and walking to the bottom would take longer than the last scoop of the mountain, next to the truck. Thus, we must create a upper bound and lower bound and take the average to find the average “on-load” time. The bounds I made were 100 minutes vs 20 minutes, hence an average of 1 hour [(100+200/2]. Thus, it takes on average, 1 hour to “on-load” the truck. Since I have already analyzed the number of times it takes to fill the truck (50,000,000), we multiply 1 hour by 50,000,000 = 50,000,000 hours, which is the total “on-load” time.

3. The last branch to analyze is the “off-load” time. However, because the activities of “on-load” and “off-load” are identical in nature, we can assume that the total “off-load” time is 50,000,000 hours as well.

Final Answer…
Total Time = 50,000,ooo hours + 50,000,000 hours + 50,000,000 hours
Total Time = 150,000,000 hours

To further break down and simplify into a more comprehensible time frame…
24 hours/day
7 days a week
Total hours in week = 24*7
To simplify math… 20 hours * 10 days = 200 hours a week
4 weeks a month
approximate total hours a month = 200 * 4 = 800 hours
total hours in 5 year = 800 hours * (12 months * 5 years) = 48,000 hours
approximate total hours in 5 years = 50,000 hours

150,000,000 / 50,000 = 3,000 (in intervals of 5 years)
3,000*5 = 15,000 years
(This answer is approximately -20% from non-rounded hours based on these same numbers)

• Renan Menezes Jan 30, 2015, 3:51 pm

Answer = # trips × amount of time per trip

(1) # trips = (1.1) mountain’s total volume ÷ truck’s volume capacity

(2) amount of time per trip = time to charge + time to discharge + (2.1) time to transport

(1.1) = height × pi × r2 (suppose it is a cone format)

(2.1.) = average speed ÷ distance

• Sri Feb 1, 2015, 2:12 am

Assuming the average mountain is 10 times the average truck bigger, and truck is moving at 60 miles per hour,
it will take 100 minutes for the truck to move the mountain

• Sri Feb 1, 2015, 2:13 am

Thank you for the question.

• adrien Feb 3, 2015, 9:21 am

I ‘ll try to work out the following estimates which I believe are necessary to answer the question :
1. Size of our average montain in cubic meters
2. Size of our average’s truck Payload in cubic meters
3. Time per trips (load, way out, off load, way back)

1. Mountain heights range up to several kms but the vast majority would be much, lower, typically under 1km.
Let’s assume our average mountain is a pyramid 1km high, with 500m square as a basis. The volume of this pyramid can be estimated that of a cube of 500m, that is 500^3 = 1,25M cubic meters (light overestimate).
2. A truck with a payload of 3*5*2 = 30 cubic meter being used
3. Each trip includes :
– loading : 25 minutes (assuming we are decently equiped to load)
– trip is 10 miles each way at the reasonable average speed of 40 miles an hour, that is 30 min (certainly slower on the way out than empty on the way back, but consider average)
– off-loading would be quicker : 5 minutes.
This addsup to a total of 1 hour per turnaround.

For the simplifying further calcualtion, we will assume our mountain is 120 M cubic meter rather than 125, which is not irrelevent given our mountain volume estimate was over the actual volume.

Caluclation goes as follow :
We would need 120 M / 30 = 4 M trips to move the mountain 10 miles away.
Spending 1hour per trip, that is 4 M hours, or a little above 80 000 days.

• Ignat Feb 4, 2015, 7:45 pm

100 years

• AAC Feb 6, 2015, 4:35 pm

The formula will be used is the following:

Estimated time (working days) = {(Transportation time/load + Loading time/load)*no. of loadings}/no.of working hours/day

> Transportation time/load = Miles (per load)/av. speed (per load)
Assumptions: av.speed = 40 miles/h
=> Transportation time/load = 20 miles /40 miles/h = 0.5 h

> Loading time/load = Load in + Load out
Assumptions: 3 workers
Av. time to load 1 cube m/worker = 0,5 h
Av. size truck volume = av. width* av. length* av. height = 1 m*3 m*1 m = 3 cube m
=> Loading time/load = 0,5 h * 2 = 1h

> No. of loadings = Average size mountain volume / Average size truck volume
Av. size mountain volume = Pyramid volume = av. length^2*av. height/3 = 100 m^2*1.500 m/3 = 15.000.000 cube meters/3 = 5.000.000 cube meters
Av. size truck volume = av. width* av. length* av. height = 1 m*3 m*1 m= 3 cube m
=> N0.of loadings = 5.000.000 cube m/3 cube m= 1.666.666,6

> No.of working hours/working day = 8 h/working day

=> Estimated time = {(0,5 h + 1h)*1.666.666,6}/8h/working day= 1.5h*1.666.666,6/8 = 312.499,9 working days = 312.500 working days

• Arnaud Trebaol Feb 12, 2015, 3:45 pm

Mountain roughly as a pyramid. of 1000m per 1000m per 1000m so 10^9 m cube of volume. The runs at 60 miles so he does 10 minutes for 10 miles. 20 Miles for Return. 10 min to charge 10 min to uncharge. 40 min. Capacity of a truck 20 m cube. so 10^9 / 20 = 5 * 10^8 travels per 40 min =2 per 10^10 minutes

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