Q. 100 - Precalculus Enhanced with Graphing Utilities

Question

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. 

Step-by-Step Solution

Answer

The car is moving at a speed of $90\mathrm{\pi }$ inches per second or $5.11\mathrm{\pi }$ miles per hour

Step 1. Given information

The radius of the wheel of the car is $15$ inches. $3$ revolutions of the wheel are done in a second.

Step 2. Required Formula

• $1$ mile = $63360$ inches
• The perimeter of the circle with radius $r$ is $2\mathrm{\pi r}$ units.
• $1$ hour = $3600$ seconds.

Step 3. Calculation

The radius is $r=15$ inches.

Therefore the perimeter of the circle is $2\times \mathrm{\pi }\times 15=30\mathrm{\pi }$ inches.

Now, the wheel does $3$ revolutions per second.

Therefore, it covers $30\mathrm{\pi }\times 3=90\mathrm{\pi }$ inches per second.

Hence, $90\mathrm{\pi }\times 3600=324000\mathrm{\pi }$ inches per hour.

That is, $\frac{324000\mathrm{\pi }}{63360}\approx 5.11\mathrm{\pi }$ miles per hour.