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# Advanced Math/Number of Revolutions- Solution/Explanation

Question

Number of Revolutions
I have attached a problem about number of revolutions with solution.  Please explain the solution.  Thanks.

The solution shows only the end result, after converting unit. It doesn't show the previous steps in which conversion factors are applied and units canceled out. I think would be clearer if the conversion factors were shown.

"In 1 min, the wheel travels π×28×n inches"
The missing details:
1 min × n rev/min × 28π in/rev = 28πn inches

"In 60 min, the wheel travels π×28×n×60 inches"
60 min × n rev/min × 28π in/rev = 60×28πn inches

"i.e. πx28×n×60/(5280×12) = 10"
(60×28πn inches)/(60 minutes) = 10 mi/hour × 5280 ft/mi × 12 in/ft × 1 hour/(60 minutes) = (10×5280×12 in)/(60 min)
(60×28πn) in = 10×5280×12 in
Then they solve for n.
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#### Janet Yang

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