Question

1. the radius of each wheel of a car is 15 inches. if the wheels are turning at the rate of 3 revolutions per second, how fast is the car moving? express your answer in inches per second and in miles per hour. round your answer to the nearest tenth.

Explanation:

Step1: Find the circumference of the wheel

The formula for the circumference of a circle is \( C = 2\pi r \), where \( r \) is the radius. Given \( r = 15 \) inches, we have:
\( C = 2\pi(15)=30\pi \) inches.

Step2: Find the distance per second

The wheel makes 3 revolutions per second (assuming the "3" was missing earlier, as the problem seems incomplete but we infer from typical problems). So the distance per second is the number of revolutions times the circumference:
\( d = 3\times30\pi = 90\pi \approx 282.743 \) inches per second.

Step3: Convert inches per second to miles per hour

First, convert inches to miles: 1 mile = 63360 inches.
Convert seconds to hours: 1 hour = 3600 seconds.
So the conversion factor is \( \frac{1\ mile}{63360\ inches}\times\frac{3600\ seconds}{1\ hour} \).
Multiply the inches per second by this factor:
\( 282.743\times\frac{3600}{63360}\approx 16.1 \) miles per hour. (We can also do it step by step: inches per second to inches per hour: \( 282.743\times3600 = 1017874.8 \) inches per hour. Then divide by 63360 to get miles per hour: \( \frac{1017874.8}{63360}\approx 16.1 \))

Answer:

In inches per second: approximately \( 282.7 \) inches per second; In miles per hour: approximately \( 16.1 \) miles per hour. (If the number of revolutions was different, adjust Step 2. Assuming 3 revolutions per second as a common case to complete the problem.)

(Note: Since the original problem had a typo or missing information (the number of revolutions per second was cut off, we assumed 3 as a common value. If the actual number is different, recalculate Step 2 with the correct number of revolutions. For example, if it was 30 revolutions per second, the answer would be different. But based on the visible text, we infer the likely number of revolutions to make the problem solvable.)