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2013 AMC 12B Problem 4

Problem 4 of 25EasierAlgebra

Ray’s car averages 4040 miles per gallon of gasoline, and Tom’s car averages 1010 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?

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Solution

If each drives DD miles, together they cover 2D2D miles using D40+D10=D8\dfrac{D}{40}+\dfrac{D}{10} = \dfrac{D}{8} gallons. The combined rate is 2DD8=16\dfrac{2D}{\frac{D}{8}} = 16 miles per gallon. Thus, the correct answer is B.

More practice

Concepts: rate · ratio and proportion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.