Question

A pick up truck is fitted with new tires which have a diameter of 42 inches. How fast will the pick up truck be moving when the wheels are rotating at 400 revolutions per minute? Answer in miles per hour.25 mph42 mph50 mph8 mph

Answer 1

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:

`l=\pi d`

Where d is the diameter of the circle. So we have:

`l=3.14\cdot42=131.88\text{ inches}`

Now we need to convert the number of revolutions per minutes to revolutions per hours, to do that we have to multiply by 60.

`\text{rev per hour}=400\cdot60=24000`

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:

`\text{speed}=131.88\cdot24000=3165120\text{ inches per hour}`

Now we need to convert this from inches per hours to miles per hour. To do this we have to divide by 63360.

`\text{speed}=(3165120)/(63360)=49.95\text{ miles per hour }`

The speed of the truck will be approximately 50 miles per hour.