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## 'One and Three' printed from http://nrich.maths.org/

Two motorboats are travelling up and down a lake at constant
speeds and turning at each end without slowing down. They leave
opposite ends A and B at the same instant, passing each other, for
the first time 600 metres from A and, for the second time, 400
metres from B.

How long is the lake (the distance from A to B) and what is the
ratio of the speeds of the boats?