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# Spin circles

HS Thomas
Ranch Hand
Posts: 3404
Four skaters spin in circular patterns of equal diameter, each a third of a mile long. They start from the four points shown by the ends of lines nearest to the circle ,at exactly the same time. They travel at 6, 9, 12 and 15 mph respectively anti-clockwise..
In 20 minutes how many times will they have simultaneously returned to the spots where they started ?

[ November 30, 2003: Message edited by: HS Thomas ]

Arjun Shastry
Ranch Hand
Posts: 1906
1
I think they won't.I am not sure.
Time required for '6' to complete one rotation: 10*pi/3 minutes
Time required for '9' to complete one rotation: 20*pi/9 minutes
Time required for '12' to complete one rotation: 5*pi/3 minutes
Time required for '15' to complete one rotation: 4*pi/3 minutes

HS Thomas
Ranch Hand
Posts: 3404
They would 3 times.
Hope that helps. Oops that was the answer. I gave it away .
Can anyone work out why ?
[ December 01, 2003: Message edited by: HS Thomas ]

Arjun Shastry
Ranch Hand
Posts: 1906
1
HS , I think its a time to post the solution.

HS Thomas
Ranch Hand
Posts: 3404
OK, here it is.
In 20 minutes they travel one third of a mile 6, 9, 12 and 15 times. The largest number these numbers are all divisible by is 3. They return to their original point 3 times in 20 minutes, after 6:40 minutes, 1.20 minutes and 20 minutes.
20 minutes is one third of an hour.
regards