2011 AMC 10A Problem 15

Question

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?

140

240

440

640

840

Let

x

be the gasoline-only distance

The miles per gallon equation is

\frac{x+40}{0.02x}=55

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.

Problem 15 in other years