2013 AMC 12B Problem 4

Question

Ray’s car averages

40

miles per gallon of gasoline, and Tom’s car averages

10

miles per gallon of gasoline. Ray and Tom each drive the same number of miles. What is the cars’ combined rate of miles per gallon of gasoline?

10

16

25

30

40

Combined mileage is total miles divided by total gallons, not the average of the two rates

If each drives

D

miles, the gallons used are

\dfrac{D}{40}

and

\dfrac{D}{10}

If each drives

D

miles, together they cover

2D

miles using

\dfrac{D}{40}+\dfrac{D}{10} = \dfrac{D}{8}

gallons. The combined rate is

\dfrac{2D}{\frac{D}{8}} = 16

miles per gallon. Thus, the correct answer is B.

Problem 4 in other years