Question

The diameter of each wheel of a bicycle is $26$ inches.

If you traveling at a speed of $35$ miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?

Answer 1

Step 1: Rewrite the given units:

Find the velocity in inches per minute:

$35$mph$=$$\frac{35}{60}$mpm

$1$mile$=$$63360$in

So,

$\frac{35}{60}$mpm$=$$\left(\frac{35}{60}\times 63360\right)$ inpm

$35$mph$=$$\left(\frac{35}{60}\times 63360\right)$ inpm

$=37134.99$ inpm

Step 2: Find the number of revolutions:

The speed of the bicycle is $\begin{array}{rcl}& & 37134.99\end{array}$inpm

So in 1-minute wheel moves $\begin{array}{rcl}& & 37134.99\end{array}$inches

The diameter (D) of each wheel of a bicycle is $26$ inches

So,

$37134.99=n\pi D$

$n$ is the number of revolutions.

$\begin{array}{rcl}37134.99& =& n\pi D\\ n& =& \frac{37134.99}{\pi D}\\ & =& \frac{37134.99}{\pi \times 26}\\ & =& 452.84\end{array}$

So, $n$ can be taken as $453$.

Hence, the number of revolutions is $453$.