Revolutions

Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?
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Revolutions
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.