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

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?

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