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

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by BTGmoderatorLU » Tue Oct 09, 2018 3:05 pm

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Source: 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

The OA is B
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by [email protected] » Tue Oct 09, 2018 7:19 pm
Hi All,

We're told that 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. We're asked for the average MILES PER GALLON that the car achieved on its trip from Town A through Town B to Town C. This question can be solved in a couple of different ways, including by TESTing VALUES.

To start, we should look to pick distances that work well with the given miles/gallon data that we have (re: 12 miles/gallon and 18 miles/gallon). Choosing 36 miles for the first part of the trip and 18 miles for the second part of the trip will make the math fairly easy.

Town A to Town B: 36 miles traveled at 12 miles/gallon --> 36/12 = 3 gallons used to travel 36 miles

Town B to Town C: 18 miles traveled at 18 miles/gallon --> 18/18 = 1 gallon used to travel 18 miles

Total miles traveled = 36 + 18 = 54 miles
Total gallons used = 3 + 1 = 4 gallons
Average miles/gallon = 54/4 = 13.5

Final Answer: B

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by Scott@TargetTestPrep » Sat Oct 13, 2018 5:19 pm
BTGmoderatorLU wrote:Source: 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
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

Alternate solution:

We can assume the distance from Town A to Town B = 36 miles (we choose 36 since it's a multiple of both 12 and 18). So the distance from Town B to Town C = 18 miles. Furthermore, the car used 36/12 = 3 gallons from A to B and 18/18 = 1 gallon from B to C.

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

average = (total distance)/(total gallons)

average = (36 + 18)/(3 +1) = 54/4 = 13.5 mpg

Answer: B

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