1954 AHSME Problem 48

A train, an hour after starting, meets with an accident which detains it a half hour, after which it proceeds at \frac{3}{4} of its former rate and arrives 3\tfrac{1}{2} hours late. Had the accident happened 90 miles farther along the line, it would have arrived only 3 hours late. The length of the trip in miles was:

\textbf{(A)}\ 400 \qquad \textbf{(B)}\ 465 \qquad \textbf{(C)}\ 600 \qquad \textbf{(D)}\ 640 \qquad \textbf{(E)}\ 550

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