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

Since the tire makes 667 revolutions per minute, the distance traveled per minute \(d\) is \(d=667\times C\). Substituting \(C = 32\pi\) inches, we get \(d = 667\times32\pi\) inches per minute.

Step3: Convert inches per minute to miles per hour

We know that 1 mile = 5280 feet and 1 foot = 12 inches, so 1 mile \(=5280\times12=63360\) inches. And 1 hour = 60 minutes.
The speed \(v\) in miles per hour is \(v=\frac{667\times32\pi\times60}{63360}\)
Simplify \(\frac{667\times32\pi\times60}{63360}=\frac{667\times\pi}{33}\)

Answer:

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