   SEARCH HOME Math Central Quandaries & Queries  Question from Emily, a student: Two swimmers start from opposite sides of the pool. Each swimmer swims the length of the pool and back at a constant rate. They pass each other for the first time 40 feet from one side of the pool and for the second time 45 feet from the other side of the pool. What is the length of the pool? Hi Emily,

The key fact here is that distance equals time times rate.

I can help get you started.

Suppose the length of the pool is $L$ feet and that the first swimmer swims at a rate of $r_1$ feet per second and the second swimmer swims at $r_2$ feet per second. Suppose that there are two time periods, the first from when they start until they pass for the first time and the second from the time they pass for the first time until they pass for the second time. Suppose that the length of the first time period is $t_1$ seconds and the length of the second time period is $t_2$ seconds.

Ok, for the first time period they start at a distance apart of $L$ feet. They start to swim. At what rate is the distance between them decreasing? How long does it take for this distance to decrease to 0 feet? Write this in terms of distance equals time times rate.

What is the total length swum by the two swimmers in the second time period? It may help to draw a diagram.

If you have difficulty completing the problem write back and tell us what you have done and where you are stuck.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.