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A certain car traveled twice as many miles from Town A to

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by AAPL » Tue Jun 25, 2019 7:52 am

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Manhattan Prep

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

OA B
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by Scott@TargetTestPrep » Mon Jul 01, 2019 4:46 pm
AAPL wrote:Manhattan Prep

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

OA B
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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by deloitte247 » Thu Jul 04, 2019 6:21 am
Let the distance between town A to B = a
Let the distance between town B to C = b
Average miles/gallon from A to b = 12
Average miles/gallon from B to C = 18
Given that 'a' is twice of 'b'
$$a=2\cdot b=2b$$
$$Required\ Average=\frac{\left(a+b\right)\cdot12\cdot18}{\left(a\cdot18\ \right)+\left(b\cdot12\right)}$$
$$Required\ Average=\frac{\left(2b+b\right)\cdot12\cdot18}{\left(2b\cdot18\ \right)+\left(b\cdot12\right)}$$
$$Required\ Average=\frac{3b\cdot216}{36b+12b}$$
$$Required\ Average=\frac{3\cdot b\cdot216}{b\cdot48}$$
$$Required\ Average=\frac{648}{48}=13.5\ \ \ \ \ \ \ \ \ \ \ Answer=option\ B$$
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