2014 AMC 10B Problem 3

Question

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}

The paved part is what remains after the gravel and dirt fractions

Set

\frac7{15}

of the trip equal to

20

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 .

Problem 3 in other years