You may also like

problem icon

Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

problem icon


A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

problem icon

Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?


Stage: 3 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Imagine that Jack is not moving and that Jill dances with the same relative speed to Jack.

Jack makes a revolution in 5 seconds, that is 72 degrees a second.
Jill makes a revolution in 6 seconds, that is 60 degrees in one second.

So Jill is turning 132 degrees per second relative to Jack.
This means that in one minute Jill will have completed
132*60/360 revolutions = 22 revolutions relative to Jack.

As Jack is half way around relative to Jill, this means they will pass 22 times in the first minute.

This problem is taken from the UKMT Mathematical Challenges.