2014 AMC 10B Problem 3

Problem 3 of 25EasierAlgebra

Randy drove the first third of his trip on a gravel road, the next

20

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

Let the path distance be

t.

Then, we get:

\begin{aligned}t &= \dfrac t5 + 20 + \dfrac t3 \\ t &= 20 + \dfrac {8t}{15} \\ \dfrac 7{15} t &= 20\\ t &= \dfrac{300}7.\end{aligned}

Thus, the correct answer is E .

Concepts: fraction · linear equation

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