AHSME 1973 Problem 29

Two boys start moving from the same point A on a circular track but in opposite directions. Their speeds are 5 ft. per second and 9 ft. per second. If they start at the same time and finish when they first meet at the point A again, then the number of times they meet, excluding the start and finish, is $\textbf{(A)}\ 13 \textbf{(B)}\ 25 \textbf{(C)}\ 44 \textbf{(D)}\ \text{infinity} \textbf{(E)}\ \text{none of these}$