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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?
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?
Age 14 to 16
Challenge Level
James from Wellingborough had the best explanation with his answer
The gerbil jumps at a rate of one jump each second, first time, and two per second, the second time, and if the labelling machine consumes tins at a constant m 'jumps' per sec and if there are j 'jumps' taken between the gerbil and the machine together then j is the rate times the time taken :
j = 20( m + 1 )
and
j = 16( m + 2 ) . . . time is 16 seconds because the gerbil makes 32 jumps at 2 jumps per second
Therefore 80 jumps, which means 81 tins if the machine is just about to take a tin when the gerbil starts or 80 tins if it just has taken one.
NRICH is part of the family of activities in the Millennium Mathematics Project.