Hi Catrina,

2.6 inches for the diameter of a car wheel seems unreasonable. I think it should be 2.6 feet.

There are 5,280 feet in a mile and 60 minutes in an hour so going 75 miles in an hour is equivalent to going $75 \times 5,280$ feet in 60 minutes. hence the speed of the car is

\[\frac{75 \times 5,280}{60} = 25 \times 264 \mbox{ feet per minute.}\]

The circumference of a circle is $\pi$ times the diameter so the circumference of the wheel is $\pi \times 2.6$ feet. Hence the car moves $\pi \times 2.6$ feet in one revolution. Thus the speed of the wheel is

\[\frac{75 \times 5,280}{\pi \times 2.6}\]

and the units are

\[\frac{\mbox{ feet / minute }}{\mbox{ feet / revolution }} = \frac{\mbox{ revolutions }}{ \mbox{ minute}}.\]

Thus the speed of the wheel is

\[\frac{75 \times 5,280}{\pi \times 2.6} \frac{\mbox{ revolutions }}{ \mbox{ minute}}.\]

How many radians are there in one revolution?

Penny