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# Help!

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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 4 inches. If there is no slippage, how many revolutions will the back wheel make while the front wheel makes 100 revolutions?

Dec 24, 2018

#1
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Converting feet to inches, we have 2.5*12=30 inches. This is for the front wheel, while the back wheel's radius is 4 inches. Revolutions come hand in hand with the circumference, so we have 2*30*pi=60pi for the front wheel and 2*4*pi=8pi for the back wheel. Now, when 60pi=100 then by indirect proportion $$\frac{60*100}{8}=\boxed{750}$$ revolutions.

Dec 24, 2018
#2
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Note : 2.5 ft =  30 in

When the front wheel makes 100 revs, the bike will travel (in inches)

100 *  2pi * 30   =    6000pi   in

So....the number of revs that the back wheel makes is

Total distance traveled  / distance traveled in one rev by back wheel  =

[ 6000 pi ]  / [ 2pi * 4 ]  =    6000/8  =  750 revolutions

Dec 24, 2018