2011 AMC 10A Problems/Problem 15

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?

(A) 140 (B) 240 (C) 440 (D) 640 (E) 840

Solution

We know that $\frac{\text{total miles}}{\text{total gas}}=55$ . Let $x$ be the distance the car traveled during the time it ran on gasoline, then the amount of gas used is $0.02x$ . The total distance traveled is $40+x$ , so we get $\frac{40+x}{0.02x}=55$ . Solving this equation, we get $x=400$ , so the total distance is $400 + 40 = \boxed{440 \ \mathbf{(C)}}$ .

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2011 AMC 10A Problems/Problem 15

Solution