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# math

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On an old-fashioned bicycle the front wheel has a radius of 2.5 feet and the back wheel has a radius of 3 inches. If there is no slippage, how many revolutions will the back wheel make while the front wheel makes 100 revolutions?

Apr 20, 2021

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First, we find how much it takes for the front wheel to make 100 revolutions, and one revolution is the length of the circumference. So we have:

$2.5\cdot12\cdot2\cdot\pi\cdot100=6000\pi$

Now, we find the circumference of the back wheel(the length of one revolution for the back wheel), and divide $6000\pi$ by that number to get our answer:

$3\cdot2\cdot\pi=6\pi$

$\dfrac{6000\pi}{6\pi}=\boxed{1000}$ revolutions.

Apr 20, 2021