Math CentralQuandaries & Queries


Question from Edward:

Hello; I have a 28.2 inch diameter tire; do not worry about engine RPM or gear ratios, please tell me what the RPM of that tire is at 8 MPH and 64 MPH. Thank you.

Sincerely; Edward

Hi Edward,

If the tire has a diameter of 28.2 inches then its circumference is $\pi \times 28.2 = 88.59 \mbox{ inches.}$ Thus the tire travels at a rate of 88.59 inches per revolution.

There are 60 minutes in an hour so 8 miles per hour is $\frac{8}{60} = \frac{2}{15} \mbox{ miles per minute.}$ There are 5280 feet in a mile and 12 inches in a foot so

\[\frac{2}{15} \mbox{ miles per minute } = \frac{2}{15} \times 5280 \times 4 = 848 \mbox{ inches per minute.}\]

One revolution is 88.59 inches so at 8 miles per hour the wheel is rotating at $\frac{8448}{88.59} = 95.3 \mbox{ revolutions per minute.}$


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