The first step we need to take is to find the length of the tires, the length of a circle can be determine by the following expression:
[tex]l=\pi d[/tex]Where d is the diameter of the circle. So we have:
[tex]l=3.14\cdot42=131.88\text{ inches}[/tex]Now we need to convert the number of revolutions per minutes to revolutions per hours, to do that we have to multiply by 60.
[tex]\text{rev per hour}=400\cdot60=24000[/tex]The tire rotates around itself 24,000 times per hour. We can multiply this number with the length of the tire in order to determine the speed in inches per hours:
[tex]\text{speed}=131.88\cdot24000=3165120\text{ inches per hour}[/tex]Now we need to convert this from inches per hours to miles per hour. To do this we have to divide by 63360.
[tex]\text{speed}=\frac{3165120}{63360}=49.95\text{ miles per hour }[/tex]The speed of the truck will be approximately 50 miles per hour.
