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# A circular rim 28 inches in diameter rotates the same number

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Manager
Joined: 30 Jan 2006
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A circular rim 28 inches in diameter rotates the same number [#permalink]  15 Apr 2006, 19:59
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A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim make in terms of x?
Manager
Joined: 09 Feb 2006
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Location: New York, NY
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A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim make in terms of x?

This is a ratio problem. If they move the same number of inches, then the smaller rim is moving a bit faster. if they move 7 inches in a second, then that is a 1/4 turn for the smaller rim, and 1/5 of a turn for the larger rim. Armed with this, we can work out a ratio for their turning. Let's set x as 1/4; The larger rim will make 12 revolutions in a minute. Therefore, in terms of x, the larger rim will turn 48x.
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Joined: 04 May 2004
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Location: India
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A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim make in terms of x?

I dont know about solution posted by jcgoodchild but if I was to face this question, I would use ratios to solve the question. the ratio of radii is 4/5 and the answer should be a multiple of 4/5 ... I might be wrong. I would really like to have opinion of other people on use of ratios.
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# A circular rim 28 inches in diameter rotates the same number

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