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2013 AMC 10B Problem 8

Problem 8 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

Let each car drive 4040 miles. Together they drive 8080 miles. Ray uses 11 gallon, while Tom uses 44 gallons, so together they use 55 gallons. The combined rate is 80÷5=1680\div5=16 miles per gallon. Thus, the correct answer is B .

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Concepts: rate · ratio and proportion

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