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Jumping Gerbils

Age 14 to 16
Challenge Level Yellow starYellow star
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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


Since it's the same j and m in each equation I can solve them 'simultaneously' to find that m is 3 and j is 80

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.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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