AHSME 1950 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: $\textbf{(A)}\ 4\text{ mph} \textbf{(B)}\ 8\text{ mph} \textbf{(C)}\ 12\text{ mph} \textbf{(D)}\ 16\text{ mph} \textbf{(E)}\ 20\text{ mph}$