Two swimmers, at opposite ends of a $90$ m pool, start to swim the length of the pool, one at the end rate of $3$ m per second, the other at $2$ m per second. They swim back and forth for $12$ minutes. Allowing no loss of time at the turns, find the number of times they pass each other.

24

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20

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Solution

The correct option is C $20$
We graph the position of each swimmer with respect to time [this graph ends with $t = 3$ (minutes)].
At the end of $3$ minutes they are back to their original positions, so that in 12 minutes this cycle is repeated four times. Since there are five meetings in this cycle, the total number of meetings is $4 \times 5 = 20$ .

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Two swimmers, at opposite ends of a 90 m pool, start to swim the length of the pool, one at the end rate of 3 m per second, the other at 2 m per second. They swim back and forth for 12 minutes. Allowing no loss of time at the turns, find the number of times they pass each other.

Two swimmers, at opposite ends of a $90$ m pool, start to swim the length of the pool, one at the end rate of $3$ m per second, the other at $2$ m per second. They swim back and forth for $12$ minutes. Allowing no loss of time at the turns, find the number of times they pass each other.