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A certain car traveled twice as many miles

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A certain car traveled twice as many miles

by BTGmoderatorDC » Mon Feb 19, 2018 8:11 pm
A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?

A. 13
B. 13.5
C. 14
D. 14.5
E. 15

I am confused about the formula to use in this problem, can some experts help?

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by GMATGuruNY » Mon Feb 19, 2018 9:47 pm
lheiannie07 wrote:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?

A. 13
B. 13.5
C. 14
D. 14.5
E. 15
Let B to C = 18 miles.
Since the rate from B to C is 18 miles per gallon, the amount of gas used from B to C = d/r = 18/18 = 1 gallon.

Since the distance from A to B is twice the distance from B to C, A to B = 2*18 = 36 miles.
Since the rate from A to B is 12 miles per gallon. the amount of gas used from A to B = d/r = 36/12 = 3 gallons.

Thus:
Average miles per gallon for the whole trip = (total distance)/(total gas) = (18+36)/(1+3) = 54/4 = 27/2 = 13.5 miles per gallon.

The correct answer is B.
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by Jeff@TargetTestPrep » Thu Feb 22, 2018 8:41 am
lheiannie07 wrote:A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?

A. 13
B. 13.5
C. 14
D. 14.5
E. 15
We are given that a certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. Thus, if the car traveled d miles from Town B to Town C, it traveled 2d miles from Town A to Town B.

We are also given that from Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon.

Thus, the number of gallons used from Town A to Town B is 2d/12 = d/6 and the number of gallons used from Town B to Town C is d/18.

Let's now determine the overall average miles per gallon, using the following formula:

average = (total distance)/(total gallons)

average = (2d + d)/(d/6 + d/18)

average = 3d/(4d/18) = (3d x 18)/4d = 54/4 = 13.5 mpg

Answer: B

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