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Age 14 to 16

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Here's a
sample of the good reasoning from Maithra of Henrietta Barnett
School, and others :

At their first crossing A has swum 30 and B has swum x - 30 , where x is the pool length.

At their second crossing A has now swum x + 20 in all and B has swum 2x - 20

There respective distances will keep in a fixed ratio because their speeds are in a fixed ratio.

This equation expresses that

and can be solved to find the
length of the pool.

x is zero or 70, and a pool of length zero is not our interest here so 70 m is the pool's length.

Here's another line of reasoning :

At first crossing A and B have swum one length between them, and A swam 30m of that length.

At second crossing A and B have swum two more lengths between them, so A will have swum 60m of those two lengths.

A has swum 90m in all, and that is one whole length plus a further 20m . So the pool is 70m long.

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?