1972 AHSME Problem 24

A man walked a certain distance at a constant rate. If he had gone \textstyle\frac{1}{2} mile per hour faster, he would have walked the distance in four-fifths of the time; if he had gone \textstyle\frac{1}{2} mile per hour slower, he would have been 2\textstyle\frac{1}{2} hours longer on the road. The distance in miles he walked was

\textbf{(A) }13\textstyle\frac{1}{2}\qquad \textbf{(B) }15\qquad \textbf{(C) }17\frac{1}{2}\qquad \textbf{(D) }20\qquad \textbf{(E) }25

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