1950 AHSME Problem 28

Two boys A and B start at the same time to ride from Port Jervis to Poughkeepsie, 60 miles away. A travels 4 miles an hour slower than B. B reaches Poughkeepsie and at once turns back meeting A 12 miles from Poughkeepsie. The rate of A was:

\textbf{(A)}\ 4\text{ mph}\qquad\textbf{(B)}\ 8\text{ mph}\qquad\textbf{(C)}\ 12\text{ mph}\qquad\textbf{(D)}\ 16\text{ mph}\qquad\textbf{(E)}\ 20\text{ mph}

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