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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?

One and Three

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

This problem stimulates students into creating some kind of diagram as an aid to visualisation. Hopefully the phrase "ratio of the speeds" will encourage students to think through how the simulation is not significantly altered if the speeds of both boats were, for example, doubled or halved. This is a useful problem for connecting speed, distance and time, and may also offer students a useful context in which to use algebra to express relationships containing known and unknown quantities.