1955 AHSME Problem 41

A train traveling from Aytown to Beetown meets with an accident after 1 hr. It is stopped for \frac{1}{2} hr., after which it proceeds at four-fifths of its usual rate, arriving at Beetown 2 hr. late. If the train had covered 80 miles more before the accident, it would have been just 1 hr. late. The usual rate of the train is:

\textbf{(A)}\ \text{20 mph}\qquad\textbf{(B)}\ \text{30 mph}\qquad\textbf{(C)}\ \text{40 mph}\qquad\textbf{(D)}\ \text{50 mph}\qquad\textbf{(E)}\ \text{60 mph}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.