$36 \cdot 33$ Two swimmers start swimming from opposite ends of a 90-foot pool, one at a speed of 3 feet per second, the other at 2 feet per second. They swim back and forth for 12 minutes. If the time to turn around is negligible, how many times do they meet?
(A) 24 .
(B) 21 .
(C) 20 .
(D) 19 .
(E) 18 .
(11th American High School Mathematics Examination, 1960)
[Sol] Solve using a graphical method. The swimming conditions of the two athletes within three minutes are as shown in the following diagram:

From the diagram, we can see: within three minutes, they meet each other 5 times.
The first person takes 60 seconds for a round trip, and the second person takes 90 seconds for a round trip. Clearly, 180 seconds is their common round trip cycle.

Therefore, within 12 minutes, the two people meet a total of 20 times. Hence, the answer is $(C)$.