Tom travels d miles by a car, whose consumption C gallons per hour is

Question

Tom travels d miles by a car, whose consumption C gallons per hour is directly proportional to the square of the speed of the car. If he travels 80% of the distance at the speed of 40 miles/hour and the remaining at the speed of 20 miles/hour, he consumes 45 gallons of fuel. How much fuel will he consume if Tom travels the whole distance d miles at the speed of 30 miles hour?

A. 30
B. 37.5
C. 50
D. 60
E. None of these

A. 30
B. 37.5
C. 50
D. 60
E. None of these

MartyMurray · Accepted Answer

Tom travels d miles by a car, whose consumption C gallons per hour is directly proportional to the square of the speed of the car. If he travels 80% of the distance at the speed of 40 miles/hour and the remaining at the speed of 20 miles/hour, he consumes 45 gallons of fuel. How much fuel will he consume if Tom travels the whole distance d miles at the speed of 30 miles hour?

A. 30
B. 37.5
C. 50
D. 60
E. None of these

Let the constant by which the speed of the car is multiplied to determine the fuel consumption per hour be k.

Also, to keep this simple, we can let the distance be 100 miles, which works nicely with 80% of the distance covered at 40 miles per hour and 20% covered at 20 miles per hour.

We get the following.

Time at 40 miles per hour: 80/40 = 2

Fuel consumption at 40 miles per hour: 40^2 × k = 1600k

Total fuel consumption at 40 miles per hour: 2 × 1600k = 3200k

Time at 20 miles per hour: 20/20 = 1

Fuel consumption at 20 miles per hour: 20^2 × k = 400k

Total fuel consumption at 20 miles per hour: 1 × 400k = 400K

Total fuel consumed at 40 miles per hour for 80% of the trip and 20 miles per hour for 20% of trip: 3200k + 400k = 3600k

Time at 30 miles per hour: 100/30 = 3 1/3

Fuel consumption at 30 miles per hour: 30^2 × k = 900k

Total consumed at 30 miles per hour for the entire trip: 3 1/3 × 900 = 3000k

Total fuel consumed at 30 miles per hour for the entire trip: 45 × 3000k/3600k = 45 × 5/6 = 37.5

A. 30
B. 37.5
C. 50
D. 60
E. None of these

Correct answer:  B

Kinshook · Answer

Blackcrow1972

Tom travels d miles by a car, whose consumption C gallons per hour is directly proportional to the square of the speed of the car. If he travels 80% of the distance at the speed of 40 miles/hour and the remaining at the speed of 20 miles/hour, he consumes 45 gallons of fuel. How much fuel will he consume if Tom travels the whole distance d miles at the speed of 30 miles hour?

A. 30
B. 37.5
C. 50
D. 60
E. None of these

How much fuel will he consume if Tom travels the whole distance d miles at the speed of 30 miles hour?

Let C gallons/hour = kv^2 ; where k is a constant and v is speed in miles/hour

Total distance = d miles

40  miles/hour
Distance = .8d
Time = .8d/40 = .02d hours
Fuel consumption rate C = k(40)^2 = 1600k gallons/hour
Fuel consumption = 1600k*.02d = 32kd

20  miles/hour
Distance = .2d
Time = .2d/20 = .01d
Fuel consumption rate C = k(20)^2 = 400k gallons/hour
Fuel consumption = 400k*.01d = 4kd

Total fuel consumption = 32kd + 4kd = 36kd = 45 gallons
kd = 45/36

30  miles/hour
Distance = d
Time = d/30
Fuel consumption rate C = k(30)^2 = 900k gallons/hour
Fuel consumption = 900k*d/30 = 30kd = 30*45/36 = 37.5 gallons

IMO B

Bunuel · Answer

Could you please provide a screenshot of the question? Thank you!

Dbrunik · Answer

let me know if this makes sense or if theres a better way.

Dbrunik · Answer

can you confirm if this is an OG question or a question from an official GMAC mock?

Blackcrow1972 · Answer

It appeared in one of my mocks.

Dbrunik · Answer

Which number mock, and was it an official GMAC mock?

Bunuel · Answer

Could you please provide a screenshot of the question? Thank you!

DanTheGMATMan · Answer

Beautiful problem. Remember the formula for direct proportion and also that fuel consumed= rate of consumption x time:

https://www.youtube.com/watch?v=1tIk5Li7eC0

Shreya_0402 · Answer

C* 0.8d/50 + C* 0.2d/100 = 45
Cd=1500
C* d/30 = 50
why is this approach incorrect?

Dbrunik · Answer

Hard to believe. This question cannot be completed in a Reasonable amount of time.

Elite097 · Answer

MartyMurray  how can k be the same for each of the speeds?

KarishmaB · Answer

\frac{Consumption}{Speed^2} = Constant C = kS^2 (in gallons/hour) We are given data of 45 gallons which is consumption in the entire journey, not gallons consumed per hour. Hence we need to find for how many hrs this consumption was maintained. Comparing Consumption in 80% of the journey with that in 20% of the journey: If distance travelled is 4 times and speed is twice, time taken will be twice too because Time = Distance/Speed C1 = k*40^2 * 2 = 3200k gallons (Total consumption in 80% of the journey) C2 = k*20^2 * 1 = 400k gallons (Total consumption in 20% of the journey) Total Consumption = 3600k gallons = 45 gallons (given) Comparing full journey consumption with that of 20% journey: If distance is 5 times and speed is 3/2, time taken = 10/3 times C3 = k*30^2*\frac{10}{3}*k = 900 * \frac{10}{3} * \frac{45}{3600} = 37.5 gallons Answer (B) Here is a video on Direct Variation used in this question: https://youtu.be/AT86tjxJ-f0

reyrest · Answer

KarishmaB

could you please help me to figure out why the below approach is wrong?

C=ks^2

I find average speed for d: 100/3 ( d/((0.8/40) + ( 0.2/20)) )

45 = k(100/3)^2

k = 45*9/(100)^2

c = k*30^2 ~ 36.45

Kinshook · Answer

Blackcrow1972

Tom travels d miles by a car, whose consumption C gallons per hour is directly proportional to the square of the speed of the car. If he travels 80% of the distance at the speed of 40 miles/hour and the remaining at the speed of 20 miles/hour, he consumes 45 gallons of fuel. How much fuel will he consume if Tom travels the whole distance d miles at the speed of 30 miles hour?

A. 30
B. 37.5
C. 50
D. 60
E. None of these

How much fuel will he consume if Tom travels the whole distance d miles at the speed of 30 miles hour?

Distance = d miles
Time = t hours
Speed = s = d/t miles/hour
Fuel Consumption C = k*s^2 gallons per hour; where k is a constant

Distance = .8d miles
Speed = 40 miles/hour
Time = .8d/40 = d/50 hours
Fuel Consumption = k(40)^2 = 1600k gallons per hour
Fuel Consumption = 1600k*d/50 = 32kd gallons

Distance = d - .8d = .2d miles
Speed = 20 miles/hour
Time = .2d/20 = d/100 hours
Fuel Consumption = k(20)^2* = 400k gallons per hour
Fuel Consumption = 400k*d/100 = 4kd gallons

Total Fuel Consumption = 32kd + 4kd = 36kd = 45 gallons
kd = 45/36 = 5/4 = 1.25

Distance = d miles
Speed = 30 miles/hour
Time = d/30 hours
Fuel Consumption = k(30)^2 = 900k gallons per hour
Fuel Consumption = 900k*d/30 = 30kd = 30*1.25 = 37.5 gallons

IMO B

Dj06 · Answer

I tried solving it by weighted average and it worked!

Average speed during the given trip = 40(4)+20(1)/5 = 36 miles per hour! (ratio is 8:2 = 4:1)

At 36 miles per hour, the consumption is 45, at 30 the consumption = 30*45/36 = 37.5!

I am not sure why it worked perfectly, I really did this so that I could eliminate options and mark a decent guess

Any insights woule be nice  KarishmaB   MartyMurray

MartyMurray · Answer

It just happened to work.

What you did doesn't really make sense.

For one thing, the average speed during the trip was not 36. It was d/((.8d/40 + .2d/20) = 33.33.

Then, we couldn't find the fuel consumption using the average speed even if we had the average speed because the fuel consumption is proportional to the square of the speed. So, different pairs of speeds that have the same average speed can be associated with different average rates of fuel consumption.

So, basically, it just so happened that the the numbers worked out when you sought to solve it that way.

MartyMurray · Answer

It doesn't work because the total fuel consumed at the average speed would not be the same as the total fuel consumed at the two speeds.

Notice that ( 2 × 1600 K) +  400 K ≠  33.33^2 K.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=87111 --- Harsha GMAT-Club-Forum-hob4qx6g.png

Tom travels d miles by a car, whose consumption C gallons per hour is

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Tom travels d miles by a car, whose consumption C gallons per hour is

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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