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2014 AMC 12B Problem 3

Problem 3 of 25EasierAlgebra

Randy drove the first third of his trip on a gravel road, the next 2020 miles on pavement, and the remaining one-fifth on a dirt road. In miles, how long was Randy’s trip?

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Solution

The fraction of the trip on pavement is 1−13−15=715. 1 - \tfrac13 - \tfrac15 = \tfrac{7}{15}. Since this equals 2020 miles, the whole trip is 20÷715=3007 20 \div \tfrac{7}{15} = \tfrac{300}{7} miles. Thus, the correct answer is E.

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Concepts: fraction · linear equation

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