AHSME 1960 Problem 34

Two swimmers, at opposite ends of a $90$-foot pool, start to swim the length of the pool, one at the rate of $3$ feet per second, the other at $2$ feet per second. They swim back and forth for $12$ minutes. Allowing no loss of times at the turns, find the number of times they pass each other. $\textbf{(A)}\ 24 \textbf{(B)}\ 21 \textbf{(C)}\ 20 \textbf{(D)}\ 19 \textbf{(E)}\ 18$