2011 AMC 10A Problem 15

Problem 15 of 25IntermediateAlgebra

Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first

40

miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of

0.02

gallons per mile. On the whole trip he averaged

55

miles per gallon. How long was the trip in miles?

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Solution

Let

x

be the distance the car drove solely on gasoline. We have that

\dfrac{40 + x}{0.02x} = 55.

Cross-multiplying and simplifying gives

40 = 0.1x

x = 400.

The total length of the trip is then

400 + 40 = 440.

Thus, C is the correct answer.