Two friends, Alan and Brian, dive in simultaneously from opposite ends of a non-standard swimming pool and swim at constant, but different, speeds.

If they first cross at a distance 30m from Alan's starting end and next cross at a distance 20m from Brian's starting end, how long is this particular pool and where will they next cross ?

Can you generalise this finding?

There are two types of crossing : head-on, as in the illustration, and overtaking. You might need to consider these separately.