Two swimmers at opposite ends of a ninety-foot pool start to swim the length of the pool, one at 3 feet per second and the other at 2 feet per second. If they swim back and forth for twelve minutes, how many times do they pass each other?

  20 times

Step-by-step explanation:

The faster swimmer can swim twice the length of the pool in ...

  (2·90 ft)/(3 ft/s) = 60 s

The slower swimmer can do it in ...

  (2·90 ft)/(2 ft/s) = 90 s

The least common multiple of these times is 180 s = 3 minutes, after which time each swimmer will be back where they started.

A graph of position vs. time shows the swimmers pass 5 times in that 3-minute period. 4 of those are passes when they are going in opposite directions. A 5th pass occurs at one end of the pool, when the faster swimmer passes the slower one going in the same direction.

Since there are 5 passes in each 3-minute period, there are 20 passes in 12 minutes.

The swimmers pass each other 20 times in 12 minutes.

step-by-step explanation: