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”
You may NOT ask any clarifying questions. Any answer that does not include a specific amount of time (days, hours, minutes, etc..) is automatically incorrect.
Good luck!
To post your reply Click Here.
(feel free to use your first name only or your initials)
** Don’t cheat by looking at everyone else’s answer first!
If you want to know what acceptable answers look like, after you post your answer look for the responses from:
Bobby, Dennis, Jakobicek, Surya, Aaron, Sachin… there are others like their answers. To see my commentary on why these answers were acceptable when others were not, click here.
{ 94 comments… read them below or add one }
← Previous Comments
Considering an average size truck needs 2 hours to drive 100 mile, in a flat road with very few trafic (no mountains in between, or curves). To transport the mountain, I would add an extra hour (i.e. it would take the truck 3 hours) as the truck driver also needs to pay attenion not to hurt anybody, or ruin anything. To accomplish this successfully the mountain would also have to have 4 wheals to make the transporation easier.
Transit time for one load:
10 mi @ 40 mi/hr = 15 min one way, 30 min round trip
+ 20min loading time (they’re professionals with good equipment)
= 50 min, round to 60 min = 1 hr per trip
Volume of mountain
Assume cone shape
Length – 6km
Width – 6km
Height – 5km higher than surrounding area (bit tall for average, but it’s a mountain, not a hill, and i skimped on the length and width)
Volume of a cone: 1/2 pixr^2 x h (off the top of my head)
= 1/2 * pi*3km^2 * 5km (round 3^2 to 10)
= 1/2 * 3* 10km * 5km = 75000 cubic meters
Pickup truck load volume
Length – 3m
width – 2m
height – 1m
volume of load: 6 cubic meters – round to 5 cubic meters
Number of truck loads to move the mountain:
75000 / 5 = about 15000 loads
15000 loads @ 1 hr/ trip = 15000 hrs
2000 hrs in regular work year = 7.5 years (3.75 yrs if they work a double shift)
Oops – lost track of my zeroes. Amend the above to be:
Volume of the mountains:
1/2 pi * 10,000m * 5000m = 75,000,000 cubic meters
Volume of truck load: 5 cubic meters
Number of truck loads: 15million
Time required: 15million hours
or 7500 years (regular work week: 40hrs/wk)
or 3750 years (double shift)
1. Well first I would first like to explore what the volume of an average mountain is:
o Mt Everest is the tallest mountain and is approx 30,000 ft and I read somewhere that a mountain needs to be roughly over 10,000 ft to qualify as a mountain, I am going to assume that the average mountain is roughly 20,000 ft high and has a slope of 45 degrees. So the vol= 1/3 * radius^2*ht= 1/3*(15000)^2*30000= 2,250,000,000,000 cubic feet (because ht= 2*radius at 45 degrees)
2. And then understand the level of effort required to move the mountain:
o For example are we digging the mountain and then moving it using the truck or is it loose dirt that can be easily divided into equal loads?
o Since I heard the word “move”, I am going to assume that the mountain has already been prepared for relocation, i.e its dug out and pulverized into equal loads
3. Thereafter, I would calculate the volume of an average truck
o When I moved last, we took an average truck and it could take 2 6 ft sofas lengthwise with room to spare so I am going to guess its 20 foot long. I also noticed that 6 ft man could stand straight in it and that it could fit a sofa and half in width. So the volume of the truck = length*breadth*height =1800 cubic feet
So an average truck will take 2,250,000,000,000/1800 = 1,250,000,000 trips
4. When we consider the time, we should think abt the following
o Time to load the mountain into the truck part by part
Assuming we use a crane with dimensions 5 ft* 3ft* 4ft = 60 cubic ft. It will take 30 moves to fill the truck per trip. Assuming that it takes 10 mins to per move, it will take 300 mins to load a truck per trip and 300* 1,250,000,000 = 37,500,000,000 mins for all the trips
o Time to drive 10 mi. Since its going to be rugged train (after all we are moving thru mountainous area!) I am going to assume a speed of 20 mph
so 10 mi/20 mph = .5 hrs = 30 mins per trip= 625,000,000 mins
o Time to unload the mountain should be the same as loading = 37,500,000,000 mins for all the trips
o Any rest stops that the driver will take and the length of a work day. I am going to only consider work hours. But if assume manhours we need to think abt the no of drivers, length of shift and break between shifts. Keeping it simple here so assuming a super worker with no break who works tirelessly
5. So total time = 37,500,000,000 + 625,000,000 + 37,500,000,000 = 75,625,000,000 mins = 143,883.18 days
Sorry: 143,883.18 yrs
Before answering this question, I would ask following questions to interviewer:
1. What according to them is an average size truck and mountain?
2. Is the mountain uprooted from ground and already loaded on that truck?
Now, answer to above questions would prove that this phenomenon is “actually” feasible according to interviewers. So, I will do the calculations after I get answer to further 3 questions:
1. What is the maximum or minimum speed of the truck?
2. How is the infrastructure quality all throughout the way to destination?
3. How is the weather and traffic in the way?
I assume that I will do simple math after I get the above questions answered.
Working in square feet, let’s imagine an “average” sized mountain is 2000 ft tall, with an equal radius (thus, over a mile around). If it’s a cone, the area will be 1/3 x base x height = 1/3 * [ ( 3.14 x 2000^2 ) x 2000 ] , which is about 8b square feet.
A pickup may be 6 feet long, about 3 feet wide, and a mound of rock could get 4 feet tall, so the area would be about 100 square feet. Therefore, we’ll need 80m trips to move the mountain. If we load the truck in an hour, unload it faster in just 30 minutes, and average around 45 miles/hr there and back (15 min there, 15 min back), the whole trip will be 2 hours. In total, we’ll need 160m hours, or 18,000 years to complete the task.
Assume average size mountain would be 2000 mtrs high, with a base of 1000 m. So the total volume would be 2*10^3*pi*500^2=500*10^6*pi=1.5*10^9 m3
Assume average trucksize to be 8*2*3=48m3; make this 50m3.
so the truck will need to drive 1.5*10^9/50= 30*10^6 times back and forth to transport the complete mountain.
Traveling 10*2=20 miles each time the truck drives makes a total of 30*10^6*20=600*10^6 miles. Assume an average truck drives 60 miles an hour –> 600*10^6/60=10*10^6 hrs is the time it will take the truck to transport the complete mountain.
Take an additional 20 minutes per transport to load and unload the truck and you get to 20 million hours for the truck to transport the mountain
Avg height 5km, base 5 km. a mountain is acone. with density twice of water. so apprx. it weights 40 bil. tones. average truck carries 10tonnes, travels the 10 mile at avg speed of 50km/h when loaded and at 80km/h when empty, so one trip of load takes appr. 20min. therefore80bil roundtrips are needed which makes appr. 14,000 years! : )
Assuming only moving time is concerned and the average speed of the truck is about 40miles per hour, then it takes about 30 minutes for one trip.
Average size of a mountain divided by average size of a truck gives the total number of trips the truck has to make.
Average size of a truck ~ one-bdr moving truck by 3x2x2.
Average size of a mountain ~ 2.e9
Time ~ 30min*1.e8 ~ 5000years
height of mountain – 1000m
radius – 20m
Volume – pi*radius2*height/3 = 1 million mtere3
density – 1 ton/metre3
weight – 1 million tonnes
capacity of truck- 10tonnes
speed of truck-40miles an hour
total time taken-50000hrs
Assumptions about mountain:
——————————————-
Height = 2000m
Area = 500 km^2
Shape = conical
Rock density = 2.5 g/cm^3 = 2.5 * 10^9 tonne/km^3
Therefore, we can now calculate the total mass of the mountain:
V = 2*500/3 = 3 km^3 (approx.)
M = V*density = 3*2.5*10^9 = 7.5*10^9 tonnes
Assumptions about truck:
——————————————-
Capacity = 25 tonnes
Av. speed = 40 mi/hr
Operation = 16 hr/day (2 8-hour shifts)
Breaks/driver change = 1 hr/day
So, effective operation = 15 hrs/day
Now, # return journeys = 7.5*10^9/25 = 3*10^8
Return time = 20 mi/40 mi/hr = 0.5 hrs
Loading/unloading time = 0.25 hrs (assumption)
So, total time/journey = 1 hr
Total time = 3*10^8 hrs
Total days = 3*10^8 hrs/15 hrs/day = 2*10^7 days
Assuming 350 working days/year,
Total years = 2*10^7/350 = 6*10^4 years
So, it would take about 60 000 years!
Size of mountain: Assume It is in shape of pyramid. with radius of 300 metres. Height 2000 metres, Hence volume = 1/3*3.14*300*300*2000= 180,000,000 m3 (approx). Assume Density = 1m3 = 1 kg.
So, in nutshell mountain is piece of rock 180,000T.
We have to break the mountain in small parts to transport it to 10 mile.
Requires 1h to break it to 1T of rock.
180,000h to break the mountain in 1T of rock(1)
Capacity of tuck: 49 Tonne truck (1 of the biggest in the industry) carry 50 T
Loading 50 T material takes 1 h
Travelling 10 miles, deloading and coming back also takes 1 h.
So loading 180,000T takes = 180,000/50 = 3600 h(2)
Similarly travelling 10 miles, deloading and coming back takes =3600 h(3)
Adding (1) +(2) + (3) = 187,200 h
P.S. My first post at this form. I hope i didnt made a mess
The tallest mountain on earth is about 29000 feet tall. Small mountains have incline requirements to be considered mountains, taller mountains have a height minimum (I think 9000 feet?). Otherwise its just a big hill. Also, I’m guessing the distribution of mountains is skewed right, with a big fat right tail bringing up the average, so I’ll go against my gut instinct to use a very small height of a couple thousand feet. So I’m going to say height is 10000 feet, the mountain is shaped like a cone and the base diameter is 20000 feet, so radius is 10000 feet.
1/3*pi*r^2*h = aprrox. 1/3*3*(100 million)*10,000=1 trillion cubic feet.
The average truck bed is 20 feet long * 10 feet wide * 5 feet deep = 1000 cubic feet
I assume we have some other large bobcat device to load the truck as soon as it gets back, so loading time is neglible.
The truck goes 60 mph for 10 miles which takes 10 minutes. Then it has to drive back another 10 minutes, for a 20 minute total round trip transit time.
It has to make 1 trillion / 1000 = 1 billion trips. 1 billion * 20 = 20 billion minutes.
20 billion / 60 = 333.333 million hours / 24 = about 13.5 million hours (its 13,888,889 hours) but i’m trying to do this in my head.
So a long time. Let’s teleport that sucker.
Assumptions
1) Avg size mountain has a height of 100 mts
2) shape of the mountain is that of a Pyramid
3) Mountain is made up of soil and rocks of uniform density – say 3 (for simplistic calculations)
4) Base of the pyramid is a square – 100X100mts^2
Volume of Pyramid = 1/3* 100* 100*100
Total mass of pyramid =( 100*100*100/3)*3=100*100*100
5) Avg truck carrying capacity is say 100
so number of trips the truck would have to make = 100* 100
now say in each trip truck would take 4 hrs ( 2 for loading, 1 for unloading, 1 for traveling 10 miles)
so total time required = 100*100* 4=40000 hrs
16-17 d
Avg Size Mountain x 10 miles/ Avg Size Truck
Avg Size Truck-Can move 2 couches, 100 lbs each—200 lbs
Avg Speed of Truck-40 mph
Pounds/Hr-Truck= 200 lbs*40 mph/10 miles= 800 lbs per hr
Kg/Hr-Truck= 800/2.2 = 800*5/6 = 133*5= 665 kg / hr ~ 6.5 * 10^2 kg/hr
Avg Size Mountain-ht 500 m, r 500 m
Volume = 1/3*r^2*h*pi~r^2*h~125*10^6 m^3
Assume: Density 1 g/cm^3 10^6 g/m^3 = 1000 kg /m^3
Stone 2x more dense than water2000 kg/m^3
Weight Avg Mountain = 125*10^6 m^3 * 2 * 10^3 kg/m^3
=250*10^9 kg
Time to Move Mountain with Truck = (2.5 * 10^11)/(6.5*10^2)= 25*10^8/6.5 ~ 4*10^8 hrs = 400 mill hrs
400*10^6 / 24 = 16.67 d
Correction-not 16-7 d. 27000 yrs approximately. Copied incorrect version of my calculation.
Time to Move Mountain with Truck = (2.5 * 10^11)/(6.5*10^2)= 25*10^8/6.5 ~ 4*10^8 hrs = 400 mill hrs
400*10^6 / 24 = 16.67 *10^6 d = 1667/365 * 10^4 yrs ~ 2.7 * 10^4 yrs = 27000 yrs
Assume an average sized truck can max load 1 ton at a time. Average sized mountain has 50 tons of rocks. So that it takes 50 loads for one truck to move the mountain.
Now let’s assume truck runs 20 miles/hour on average when fully loaded (include acceleration and deceleration time on a short distance trip of 10 miles), and 40 miles/hour when empty. So 10 miles each way, average driving time per load is 45 (30mins+15mins) minutes. Also assume loading and unloading the 1 tons of rocks take half an hour each time, so that’s an hour. In total, one load round-trip takes 1 hour and 45 mins, or 1.75 hours. 50 loads then take 50*1.75=87.5 hours
For the purposes of the discussion, I am going to assume the following..
- Volume (or capacity) of the truck is the limiting factor rather than weight (no super heavy rocks).
- Loading / unloading is the limiting factor rather than breaking the mountain apart or clearing the mountain of trees, access issues et al
- truck when loaded or unloaded will travel at 60mph or travel 10 miles in 10 mts
- Typical mountain is a pyramid… at 500 m radius and 1000 m height. so volume is 1/3 * 3.14 * 500*500* 1000
- Truck is a 10 m * 10m * 15 m
- So # of truck loads in the mtn is 1.6 * 10^5
- Total time to move the mountain = (loading time in mts + 10 mts transportation + unloading time) * # of truck loads
- assuming 10 mts for loading and unloading.. this turns out to be 20 mts * 1.6 * 10^5 = 3,200,000 mts… or 53,000 hrs or 2,200 days
Average mountain is cone shaped.
Truck (dumpster) has a rectangular box-shape of holding area, that will be used to move the rocks/rubble from the mountain.
Assumptions:
Mountain size: height = 150m, radius of base = 100 m. Therefore volume of rubble – 1/3*pi*r^2*h
Volume = 1554,300 cu metres.
Truck size = 10 x 6 x 3 = 180 cu metres. In one trip, truck can move 180 cu metres of mountain
Ignoring the skillset/time required to re-build the mountain, and assuming that for one trip, truck takes 30 mins (area would be hilly) to cover the 10 miles and that 1.5 hours are taken to load and unload the truck, the truck can make 6 trips in a 12 hour day.
Moving 180 cu metres per trip, truck needs 8635 trips in total, to move all 1,554,300 cu metres of rubble.
At the rate of 6 trips per day, truck needs 1439 days to make 8635 trips.
Average Weight of the Mountain = 10000 tons
An average truck can move at one time = 1 ton
Time taken to load truck = 30 min
Time taken to unload truck = 30 min
Time taken to travel a dist of 10 miles = 30 min
Time taken to move 1 ton of the mountain = 30*2 (travel time) + 30 (load) + 30 (unload) = 2hrs.
Time to move mountain ~ 20000 hrs
1. Estimate the volume of average mountain:
Mountains are usually kinda cone-shape, so let’s assume that we can caculate its volume as a cone. For average mountain, I would assume the height is 400 meters and the diameter is 1000 meters. Then the volume would be 3.14X (1000/2)2(square) X 400 X1/3=~100,000,000 cube meters
2. Estimate the loading capacity of an average truck:
The truck trunk is usually a rectangle with a length of ~10 meters and a width of ~6 meters. Assume that the truck can load a height of ~3 meters. Then for 1 load, the volume is 10X6X3=180 cube meters
3. Calculate the number of loads the truck need to move the mountain:
100,000,000/180=555556 loads
4. Estimate the average time per load
Assume the average speed is 50 miles/hour
The loading time is 20 minutes
The unloading time is 10 minutes
Total time for each load is 60X10/50+20+10=42 minutes
5. Total time needed:
42 minutes X 555556=233352 minutes = ~4.43 years
Estimating:
1) a mountain have 10,000,000 TN
2) a Truck load can move 10 TN
3) the time to load, move and unload the truck is about 2 hr
10,000,000tn / 10tn, truck load = 100,000 truck loads
100,000 truck loads/ 4 truck loads, day = 250,000 days
Moving a mountain to an nearby location will take approximately
250,000 days
If we assume the mountain to be a cone, high 2000 metres, and large 14000, its volume is 28000*pi = about 90000 m^3. If we assume that an average truck can load 3*2*1.5 = 9 m^3, it would need 10000 travels to move the mountain.
Assuming half an hour to load the car, an hour to go from the top of the old to the top of the new mountain, and half an hour to unload it, each travel is 2 hours long. Therefore the total amount of time is 20000 hours = 3 years, 238 days, 8 hours. That is, almost 4 years.
lol. I would like to point out my errors:
1) in the initial multiplication I’ve forgot 3 zeros! Then the final result is going to be something close to 3700 years! This type of error is the safest way to fail an interview.
2) I’ve forgot the way back for the truck, another hour. Then I should multiply 3700 * 1.5 = 5550 years!
Assuming:
– avg mountain height: 4 km
– avg slope: 45 deg
– mountain shape can be approximated as a cone
– body of the truck: 2m (w) x 8m (l) x 1.5m (h)
– avg speed of the truck when full: 30 mph
– avg speed of the truck when empty: 50 mph
Since the avg slope is 45 deg, radius and height are the same.
The volume of the mountain is radius*height*pi ~= 50 km^3.
The volume of the body of the truck is ~25m^3.
Total round-trips: 50km^3/25m^3 = 2000
If we assume to have machinery so that loading/unloading times are negligible, we end up having: 2000*(10mi/30mph + 10/50mph) ~= 10^3 hrs ~= 40 days (or 125 days working 8 hours per day).
First of all we need to Know what is the mass of an average mountain.
The average density of a rock is Higher than water’s which is d=1
So we can suppose it is roughly d=2tn/m^3
We can suppose that a mountain’s figure is a cone. So V= π* r^2 * h
An average mountain’s height is about 1000m, and radius r= 5000m .
So the volume of our average mountain is V= 78500000000m^3
m=d*V=157000000000tn
the average truck carries 10tn.
Lets suppose that the average time to load, transfer and unload is 5hours
the truck has to repeat the action 15700000000 times
So it needs 31400000000 hours= 3584474 years
Lets assume, that we can explode the mountain, thus time for breaking the mountain into carryable pieces is zero. Then lets estimate:
volume of average mountain= 2.5km*1/3*((1.7*2.5*km)^2)*Pi=
=50 cubic km. (approximately)=50 000 000 000 cubic m
volume of averagge truck is 2m*2m*6m=24 cubic m
time for the 10miles trip = half hour (assume there are no good roads near the mountain)
time for filling the truck (by another machine) = (24/1/7)*15seconds= 45 minuts
+ overhead near 10 minuts every trip
TIME= 1.4 hours * (50 000 000 000 /24)= (200 000 000 000 ) /96 *1.4=
= 280 000 000 0 hours approximatley = more then 100 million days
Volume of Mountain: 1,000,000 cubic meters
Volume of truck: 20 cubic meters
# of one way trips: 50,000
Trip time:10mp for 10 km 1 hour
Total one way trip time: 50,000 hours (A)
Total Return trip time: @20mph: 25,000 hrs (B)
Total Trip Time:75000 Hours
Dwell time per trip on each end: 5 minutes (Load Unload etc)
Total Dwell: 5*2*50000= 500,000 minutes= 8500 hours say 9000 hours
Mountain Breaking and assembling time: 0 minutes assume that work is done while truck is in transit
total time: 75000+9000 hours=84000 hours= 3500 days
300 days
I assume that an average mountain is a 1 km long, 200 m and 50 m wide. It tapers uniformly as we move up its height. So that gives me a volume = .5*50*200*1000 cubic meters = 5000000 cubic meters.
Now I would estimate the volume that an average truck could carry. I assume that loading portion of an average truck is 5m long, 3 m wide and 2.5 m high. That gives me 37.5 cubic meters.
Now I would assume that, keeping in mind the obstacles and jams, the average speed of the truck is 20 miles/hr. So for an up and down trip of 20 miles (10 miles up and 10 miles down) it will take an hour. It will takes about 30 min to load and 30 min to unload. I will assume that mountain is cut and the truck does not have to wait just because the mountain is uncut at any moment. So to carry 37.5 cubic meters of the mountain it takes 2 hours.
Assuming the work continues 24*7 in three shifts. So daily 12*37.5 cubic m of the mountain could be moved. That gives me 450 cubic meters of mountain per day. So number of days it will take to transfer the whole mountain would be 5000000/450, i.e. 11111 days.
Suppose the mountain consists of solely stones and soil, moreover, it has a cone shape. Assume the radius of bottom is r=25m, and the height is h=300m. Using the formula V= (Pi)x(r^2)xh , we have the volume of the mountain being 3.14 x 625 x 300= 588,750m^3. Let’s approximate again the capacity of a truck is V=length x width x height = 10 x 5 x 10 = 500m^3. Suppose we have 100 labor, it will take them 30 minutes to fill up the truck at one time, now 10miles=16.09km. Using common sense, it takes me 1.5h to get from my apartment to CDG airport in Paris by bus, the length is 29km. The time is roughly 16.09×1.5/29=50 minutes for the truck to reach destination. Total time for transportation in one go is 50+30+50=130minutes
There are 1,178 repeated times to clear the mountain. (588,750/500=1178) This means it’d take 1178×130/60= 2553 hours. The average working hour per day is 8, so 2553/8 = 320 days
First we need to determine how much material there is in the mountain and how much the truck can hold. Let’s assume that an average mountain is approximately cone-shaped and is 1,000 feet high with a radius of 500. If the cone formula is 1/3 base * height, this gives us an area of approximately 500,000 feet squared (1/3 * 1,000*500). An 18-wheeler truck could hold perhaps 500 square feet of material. [Note: I chose these numbers because they are relatively easy to work with but they could be way off -- I would verify that my assumptions are reasonable with the interviewer.] This means that it would take 1,000 trips for the truck to move the mountain.
Each trip can be broken into 4 parts: loading the truck, traveling the 10 miles, unloading the truck, and traveling back. We don’t know how many people we have doing the loading — let’s assume that we have a big crew and they can load up the truck in 1 hour. Since the truck is driving to a mountain, it’s probably not on a highway, so I’ll assume it’s going 40 miles an hour and can make the 10-mile trip in 15 minutes. Unloading the truck would also take 1 hour, and traveling back would be another 15 minutes. This gives us a total of 2.5 hours per trip. Multiplied by 1,000 trips = 2500 hours, or approximately 104 days. (2400 hours = 100 days, 100 leftover hours = ~4 days.)
To determine the duration of the move, we need to know the duration of each trip and the number of trips needed:
Total duration = (# trips) * (duration of a trip)
The first element; the # of trips can be calculated by dividing the size of the mountain by the size of the truck:
# trips = (size of mountain) / (size of truck)
The second element; the duration of a trip, is the sum of several components:
- Duration of filling the truck
- Duration of the trip to the new location
- Duration of unloading the truck
- Duration of the trip back
- Overhead (truck breaks down, truck has to get gas, getting the materials ready in the morning, preparing for the night after the work day etc.)
So let’s look at each of the two main components individually to get an estimate.
1. # of trips necessary to move the mountain
a. Size of truck
Let’s say the bed of the truck has a volume of 5m*3m*2m = 30m^3. For efficiency, we will pile up high and get about 50m^3 of earth into the truck.
b. Size of the mountain.
Let’s assume the mountain is a cone shape. The height is about 1400m and the radius is therefore 1000m. The volume of a cone is 1/3*pi*r^2*h, which is 1/3 * 3.14 * 1E6 m^2 * 2E3 m. This is about 2E9 m^2.
===> Total number of trips necessary is 2E9 / 50 = 40 million
2. Duration of a trip
Here we have to make a couple of strong assumptions. First of all, I’m going to assume that the new location of the mountain is a little under an hour’s drive away from the old one. I am going to assume a 8-hour work day. I will assume the following numbers for the different parts of the trip:
- Duration of filling the truck: 0.1 workday
- Duration of the trip to the new location: 0.1 workday
- Duration of unloading the truck: 0.1 workday
- Duration of the trip back: 0.1 workday
- Overhead: 0.1 workday
The total of a trip then comes to 0.5 workday, which means we can make 2 trips per workday.
===> T0tal number of working days necessary to move the mountain (with 1 truck): 20 million
Let’s assume the following:
average size truck:
Load 8m3
speed 30 mph
average size mountain:
Piramid shape
height 1000m
basis square 1000m x 1000m
Volume to be transported:
V = 1/3 (B x H) = 1/3 (1.000.000.000) m3 = 333.333.333 m3
Time needed:
Load/Unload = 10 min
Load + unload + go to + go from = 10 + 10 + 20 + 20 = 60 min = 1h
Time needed is one hour per one truck load
Total time needed with one truck = (1h x 333.333.333 /
= 41.666.667h
I’ve tried to do this in as few moves as possible. As no follow up questions are allowed, and little detail is provided (and also from reading the above responses) it is clear that endless variations in assumptions are available, and is it normal to to sit in front of an interviewer for 15 minutes in silence while you mull over these in your head? Plus I am not a maths or science person!
Remembering that MC is the best solution available in the time available with the information available, I assumed that anything we haven’t been given details on is outside scope, and all that is at your disposal is one average truck. Therefore all that really matters is the volume of the truck, the volume of the mountain, and the amount of time it takes to move that volume 10 miles.
Average mountain – 3,500 metres.
As its triangular, I guessed its volume from halving that of a cube with sides all equalling 3,500m – i.e. 3,500 cubic metres / 2 = 1,750 cubic metres.
Assumed each cubic metre of dirt/gravel would weigh 1 tonne i.e. 1000 kg.
Your average moving truck has a load of 3 tonnes.
1,750 / 3 = approx 580 truckloads.
10 miles equals approx 20 kilometres.
Say the truck travels at 60km/h, making a one way trip 20 minutes and return 40 minutes.
580 x 40 minutes = 23,200 –> i.e. approx 400 hours.
Taking into account an average 8 hour work day – 400/8 = 50 days.
I.E. 50 working days of one truck in constant movement, not taking into account loading time, quarrying, labour constraints etc etc etc.
I would do the following:
1. Estimate the size of an average mountain and divide it into smaller geometrical shapes- rectangles or smaller triangles
2. Estimate the size of an average truck and estimate the volume it can transport. Volume would be in iterms of rectangles or triangles
Make assumptions:
1. Assume an avg speed of the truck
2. Assume the time of loading of the truck
3. Assume there are no roadblocks in the path of the truck
4. Assume there is enough resource availability
Answer would be: Time for breaking the mountain for the first delivery+ time for loading
Oops- Sent submit too early for the previous post.
Answer would be: Time for breaking the mountain+ time for loading the truck+time for truck’s transportation and back
It’s only 10 miles. So you can move the mountain just by moving part of its bottom. Let’s cut the mountain into horizontal layer, and then shift the most bottom layer 10 miles to any direction. The layer shape would be cylinder. All we have to do is to move half of its side to the opposite side. Let’s guess the volume of such part. Let’s say the mountain have r=500m. Half of the cylinder length is (pi)*r = 3.14*500 = 1,570 m. Say the height of the cylinder is 20m, and the depth (towards inside the cylinder) is around 5 m. Thus, 1,570*20*5 = 157,000 m3 to move.
Now let’s guess the volume of a dump truck, let’s say it’s 5 m * 3 m * 1.5 m = 22 m3.
It depends on how many trucks do we have. Given 10 trucks, it’ll take 714 times to move the soil volume.
If one truck can move back and forth 10 times in one day (include load and unload, and smooth road, and rest time – we have relief crew, it’ll take 71 days to move the mountain 10 miles.
Average size of the mountain = 1000^3 ft
Average size car’s carrying load = 5^3 ft
Distance for one trip = 10 miles * 2 (for return trip) = 20 miles
Estimated speed = 60mph
Estimated time to travel for one trip = 20 minutes
Time to unload = 10 minutes
Total time for one trip = .5 hours (20 + 10 minutes)
One trip bring 5^3 feet, so taking 1000^3 feet would take (1000/5 )= 200 trips
Each trip takes a half hour, so it would take about 100 hours of consistent work. Factoring in 10 hour work days, it would take 10 days to complete
730 days
Average mountain has the height of 1000 m and the base in the shape of circle with radius 50 m. Then, the volume of the mountain is equal to 1/3*3,14*50^2*1000. When we round it, it’s about 2500000m 3. he average truck has dimension: 10x3x2=120m3. Then, we know that we need around 21000 trucks. To load and unload the truck we will need 20 minutes and to go back and forth(so it’s 20 miles) we need 40. So it’s one hour for one truck, hence it’s 21000 hours/24=875 days = 2 years and 4 months (rounded)
Assume a truck can charge a max of 5x3x2= 30 m3
Assume a mountain ,1000m high, with cone shape, radius 5,000m
> volume mountain = 1/3 pi r2 h = (5,000)2 x 1000= 25,000,000,000 m3
Number of truck loads needed, c.a. 1B
Assume material to be moved is prepared while truck travels back and forth
Assume truck takes 1 hr to load, travel, unload, travel back
> 1,000,000,000 hours
Assume 10 hrs work per day
> 100,000,000 days
300,000 years!
Each two-way trip: 20miles
At an average speed of say 40MPH, each trip would take 30min.
Now, considering an average mountain to have a volume of 1 cubic mile and a truck to have a volume of 1000 cb ft, it would take 1cbmi /1000 cbft *5280^3 cbft/cbmi = 125 *30min= 3750 min.
← Previous Comments