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On the Road

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

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There and Back

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?

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Escalator

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?

Swimmers

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.