Question

A car that has a wheel radius of 1. 5 feet travels 30 miles in 45 minutes. How fast are the wheels spinning? Give your answer in revolutions per minute. ​

Answer 1

373.5 rpm

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.

`\frac{30\text{ mi}}{45\text{ min}}*\frac{5280\text{ ft}}{1\text{ mi}}*\frac{1\text{ rev}}{\pi(3\text{ ft})}=\frac{30\cdot5280\text{ rev}}{45\cdot3\pi\text{ min}}=\boxed{(3520)/(3\pi)\text{ rpm}\approx373.5\text{ rpm}}`

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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.