# Spin circles

HS Thomas

Ranch Hand

Posts: 3404

posted 12 years ago

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 ]

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: 1899

1

posted 12 years ago

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

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

MH

HS Thomas

Ranch Hand

Posts: 3404

Arjun Shastry

Ranch Hand

Posts: 1899

1

HS Thomas

Ranch Hand

Posts: 3404

posted 12 years ago

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

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