2014 AMC 10B Problem 3

Below is the professionally curated solution for Problem 3 of the 2014 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 10B solutions, or check the answer key.

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Concepts:fraction linear equation

Difficulty rating: 900

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?

$30$

$\dfrac{400}{11}$

$\dfrac{75}{2}$

$40$

$\dfrac{300}{7}$

Solution:

Let the path distance be $t.$ Then, we get: $\begin{align*}t &= \dfrac t5 + 20 + \dfrac t3 \\ t &= 20 + \dfrac {8t}{15} \\ \dfrac 7{15} t &= 20\\ t &= \dfrac{300}7.\end{align*}$

Thus, the correct answer is E .

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