Q. 99 - Precalculus Enhanced with Graphing Utilities

Question

The diameter of each wheel of a bicycle is $26$ inches. If you are traveling at a speed of $35$ miles per hour on this bicycle, through how many revolutions per minute are the wheels turning? 

Step-by-Step Solution

Answer

The wheels are turning in $453$ rotations per minute.

Step 1. Given information

The diameter of the cycle is given as $d=26$ inches and the the speed of travelling is $35$ miles per hour.

Step 2. Required Formula

• $1$ mile = $63360$ inches.
• Radius of a circle $r=\frac{d}{2}$, where $d$ is the diameter of the circle.
• The perimeter of the circle with radius $r$ is $2\pi r$ units.

Step 3. Calculation

As the wheel of the cycle is circular, the path covered by one rotation of the wheel is the perimeter of the circle.

One rotation means $2\pi r=2\pi \frac{d}{2}=2\pi ·\frac{26}{2}=26\pi$ inches.

Speed of the cycle is $35\times 63360$ inches per hour.

Therefore, $\frac{35\times 63360}{60}=36,960$ inches per minute.

Now, $26\mathrm{\pi }$ inches are covered in 1 minute.

Therefore, $36,960$ inches are covered in $\frac{36,960}{26\mathrm{\pi }}=\frac{36,960\times 7}{26\times 22}\approx 452.3$ 

Therefore, $453$rotations are done in a minute.