2013 AMC 12B Problem 4

Below is the professionally curated solution for Problem 4 of the 2013 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 12B solutions, or check the answer key.

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Concepts:rate ratio and proportion

Difficulty rating: 1220

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?

$10$

$16$

$25$

$30$

$40$

Solution:

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 $\dfrac{2D}{D/8} = 16$ miles per gallon. Thus, the correct answer is B.

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