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Jack dances clockwise around the Maypole, making one revolution every five seconds.
Starting from a point diametrically opposite Jack's starting point, Jill dances anticlockwise, making one revolution every six seconds.

How many times do they pass each other in the first minute?
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.