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# Swimmers

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Age 14 to 16

Challenge Level

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.Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. ... How many steps are there on the escalator?