Answer:
373.5 rpm
Step-by-step explanation:
You want the rotational speed of a 3 ft wheel traveling 30 miles in 45 minutes.
Units conversion
We want to multiply by factors that eliminate units we don't want and replace them with units we do want.
[tex]\dfrac{30\text{ mi}}{45\text{ min}}\times\dfrac{5280\text{ ft}}{1\text{ mi}}\times\dfrac{1\text{ rev}}{\pi(3\text{ ft})}=\dfrac{30\cdot5280\text{ rev}}{45\cdot3\pi\text{ min}}=\boxed{\dfrac{3520}{3\pi}\text{ rpm}\approx373.5\text{ rpm}}[/tex]
__
Additional comment
The circumference of the wheel is ...
C = πd . . . . . where d is the diameter, or twice the radius
The distance the wheel travels in one revolution is the length of its circumference.
The size of a wheel is given by its diameter. A "3 ft wheel" has a diameter of 3 feet, or a radius of 1.5 feet.
