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

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.