The first step we need to take in order to solve the question is to calculate the length of the wheel. The length of a circle cna be found with the following expression:
[tex]\begin{gathered} l=2\cdot\pi\cdot r^{} \\ l=d\cdot\pi \end{gathered}[/tex]
The diameter of the wheel is 24 inches, therefore:
[tex]\begin{gathered} l=24\cdot\pi \\ l=24\pi\text{ in} \end{gathered}[/tex]
Each complete turn on the wheel moves the truck 24*pi inches. The wheel is turning at a rate of 455 rotations per minute, therefore in one minute the distance traveled by the truck is:
[tex]\begin{gathered} v=455\cdot24\cdot\pi \\ v=10920\cdot\pi\text{ in/min} \end{gathered}[/tex]
The speed of the truck is 10920*pi inches per minute. We need to convert this to miles per hour. To do that we need to divide the expression by 1056.
[tex]\begin{gathered} v=\frac{10920}{1056} \\ v=10.34\cdot\pi\text{ mi/h} \end{gathered}[/tex]
The speed of the truck in miles per hour is 10.34*pi
