AMC 12 2014b Problem 3

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?

\textbf{(A)}\ 30 \textbf{(B)}\ \frac{400}{11} \textbf{(C)}\ \frac{75}{2} \textbf{(D)}\ 40 \textbf{(E)}\ \frac{300}{7}