1963 AHSME Problem 20

Two men at points R and S, 76 miles apart, set out at the same time to walk towards each other. The man at R walks uniformly at the rate of 4\tfrac{1}{2} miles per hour; the man at S walks at the constant rate of 3\tfrac{1}{4} miles per hour for the first hour, at 3\tfrac{3}{4} miles per hour for the second hour, and so on, in arithmetic progression. If the men meet x miles nearer R than S in an integral number of hours, then x is:

\textbf{(A)}\ 10 \qquad \textbf{(B)}\ 8 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 2

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