2007 AMC 12B Problem 2

Below is the professionally curated solution for Problem 2 of the 2007 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 12B solutions, or check the answer key.

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Concepts:distance rate and time harmonic mean

Difficulty rating: 990

A college student drove his compact car $120$ miles home for the weekend and averaged $30$ miles per gallon. On the return trip the student drove his parents' SUV and averaged only $20$ miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?

$22$

$24$

$25$

$26$

$28$

Solution:

The trip home uses $120/30=4$ gallons, and the return trip uses $120/20=6$ gallons.

The round trip covers $240$ miles on $10$ gallons, so the average is $\dfrac{240}{10}=24 \text{ miles per gallon.}$

Thus, the correct answer is B.

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