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Weekly Problem 30 - 2006

Stage: 3 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.

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