How many more revolutions?

Mathematics
Tutor: None Selected Time limit: 1 Day

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 2nd, 2015

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

First we will calculate the circumference of both wheels.since the distance covered by one complete revolution is equivalent to the circumference of the wheel involved

circumference=πd

1st wheel= 3.142*16=50.2655 inches

2nd wheel=3.142*27= 84.8230 inches

Now we find out how many revolution each wheel makes.

But first we convert the miles to inches

1 mile= 63,360 inches

therefore  4,264.5 miles will be equal to 270,198,720 inches

Next we find how many revolution each wheel goes.

1st wheel= 270,198,720/50.2655=5,375,430.86212= 5,375,431(rounded off to the nearest whole number)

2nd wheel= 270,198,720/84.8230=3,185,441.68445=3,185,442(rounded off to the nearest whole number)


The 16 inch will will make (5,375,431-3,185,442)

=2189989 revolutions

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 2nd, 2015

The 16 inch will will make (5,375,431-3,185,442)

=2189989 revolutions more than the 27 inch wheel


Sep 2nd, 2015

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Sep 2nd, 2015
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Sep 2nd, 2015
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