How many more revolutions?

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The Northern Tier bicycle tour route from Anacortes, Washington, to Bar Harbor, Maine, is a 4,264.5 miles long. How many more revolutions over the entire route will a 16-inch diameter wheel on a bike trailer complete when compared with a 27-inch diameter wheel on a bicycle? Please show work and explain your process step by step and the reason why you took those steps. 

Also... What's a revolution? I know I've heard of the American Revolution in my History class.. But I'm not sure in math...

Sep 3rd, 2015

Thank you for the opportunity to help you with your question!

The distance to be covered is 4264.5 miles

for us to find the number of revolutions that the 16 wheel diameter will cover, we first calculate the circumference of the wheel

circumference = piD where pi=3.142

hence circumference = 3.142*16= 50.272 inches = 0.0007934 mile

number of revolutions = distance covered/circumference = 4264.5/0.0007934 = 5374968 revolutions

for the other wheel

circumference = 3.142*27 = 84.834 = 0.0013389 mile

number of revolutions = distance covered/circumference = 4264.5/0.0013389 = 3185077 revolutions

The 16 inch diameter wheel will complete 2189891 revolutions. this is obtained by subtracting the two revolutions.

A revolution is a complete cycle made by the wheel.


Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 3rd, 2015

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