Question

The diameter of each wheel of a bicycle is 27 inches. If you are traveling at a speed of 10 miles per hour on this​ bicycle, through how many revolutions per minute are the wheels​ turning?

Answer 1

`RPM~=124.5`

Explanation:

.

The perimeter (circumference) of the wheel is:

`P=2pir=pid=pi(27)=27pi` in

This is also the distance the bicycle travels with each revolution of the wheel.

To figure out the number of revolutions of the wheel over a distance of `10` miles, we convert the `10` miles to inches and divide it by `P`:

`1` mile `=63360` inches

`10(63360)=633600` inches

`RPH=633600/(27pi)` (this is the number of revolutions in one hour)

We divide this by `60` to get the number of revolutions per minutes or `RPM`:

`RPM=(633600/(27pi))/60=(633600/(27pi))(1/60)=10560/(27pi)=10560/84.823=124.49`