Question

the radius of the tires of a car is 16 inches, and they are revolving at the rate of 667 revolutions per minute. how fast is the car traveling? a. \\(\frac{2668}{11}\pi\\) mph b. \\(\frac{667}{33}\pi\\) mph c. \\(\frac{667}{66}\pi\\) mph d. \\(\frac{667}{330}\pi\\) mph

Explanation:

Step1: Calculate the circumference of the tire

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r = 16\) inches, so \(C=2\pi\times16 = 32\pi\) inches.

Step2: Calculate the distance traveled per minute

The tire makes 667 revolutions per minute. The distance traveled per minute \(d_{min}\) is the number of revolutions times the circumference. So \(d_{min}=667\times32\pi\) inches.

Step3: Convert inches per minute to miles per hour

We know that 1 mile \( = 5280\times12\) inches (since 1 mile \(= 5280\) feet and 1 foot \( = 12\) inches) and 1 hour \(=60\) minutes.
The speed \(v\) in miles per hour is:

$$
LATEXBLOCK0
$$

Answer:

B. \(\frac{667}{33}\pi\) mph