2014 AMC 12B Problems/Problem 3

Problem

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

$\textbf{(A)}\ 30\qquad\textbf{(B)}\ \frac{400}{11}\qquad\textbf{(C)}\ \frac{75}{2}\qquad\textbf{(D)}}\ 40\qquad\textbf{(E)}\ \frac{300}{7}$ (Error compiling LaTeX. Unknown error_msg)

Solution

If the first and last legs of his trip account for and of his trip, then the middle leg accounts for ths of his trip. This is equal to miles. Letting the length of the entire trip equal , we have