Problem: Two swimmers, at opposite ends of a -foot pool, start to swim the length of the pool, one at the rate of feet per second, the other at feet per second. They swim back and forth for minutes. Allowing no loss of time at the turns, find the number of times they pass each other.
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Graph the position of each swimmer with respect to time [this graph ends with (minutes)]
At the end of minutes they are back to their original positions, so that in minutes this eycle is repeated four times. Since there are five meetings in this cycle, the total number of meetings is .
The problem may be viewed as one in periodic phenomena; the period for the faster swimmer is seconds, while the period for the slower swimmer is seconds the period is the time-interval necessary for tie swimmer to return to his starting point). The common period is seconds or minutes.