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A circular wheel 28 inches in diameter rotates (moves) the same number of inches per second as a circular wheel 35 inches in diameter. If the smaller wheel makes x revolutions per second, how many revolutions per minute does the larger wheel make in terms of x?

A circular wheel 28 inches in diameter rotates (moves) the same number of inches per second as a circular wheel 35 inches in diameter. If the smaller wheel makes x revolutions per second, how many revolutions per minute does the larger wheel make in terms of x? Correct Answer 48x

Let the revolutions made by larger wheel per minute be R. Circumference of smaller wheel, 2 π r = 2 x π x (28/2) = 28π Circumference of larger wheel, 2 π r = 2 x π x (35/2) = 35π  Speed of smaller wheel per minute = 60x Distance covered by larger wheel per minute = Distance covered by smaller wheel per minute or, R x 35π  = 28π x 60x or, R =  28π x 60x / 35π = 48x  

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