How long would a track be?

I recall a similar problem from the Moscow Puzzles. A clever way of solving with minimal algebra is as follows:

When they pass each other first, they have together crossed $1$ length of the pool. When they cross again, they have crossed $3$ lengths of the pool, and since their speeds are constant, we know that it took $3$ times as long.

So in the whole time elapsed, swimmer A traveled $84*3=252$ feet and met $36$ feet from his starting point. Thus $2L=252+36$ and $L=144$.

Let the length of the pool be $L$. When they first meet, $A$ has swum $84$ feet and $B$ has swum $L-84$. How far have they each swum the next time they meet? Now require that the speeds be constant, so the ratios of distances are the same at each meeting. That gives an equation in $L$.