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To solve this problem, we'll use the given information to calculate the bicycle's speed in miles per hour (mph).

1. **Find the circumference of the tire:**
   - The radius \( r \) of the tire is 13 inches.
   - The circumference \( C \) of a circle is given by \( C = 2\pi r \).

   \[
   C = 2\pi \times 13 \approx 81.68 \text{ inches}
   \]

2. **Calculate the distance traveled per minute:**
   - The tire turns at a rate of 215 revolutions per minute (rpm).
   - Each revolution covers the circumference of the tire.

   \[
   \text{Distance per minute} = 215 \times 81.68 \approx 17561.2 \text{ inches per minute}
   \]

3. **Convert the distance from inches per minute to feet per minute:**
   - There are 12 inches in a foot.

   \[
   \text{Distance per minute} = \frac{17561.2}{12} \approx 1463.43 \text{ feet per minute}
   \]

4. **Convert the speed from feet per minute to miles per hour:**
   - There are 5280 feet in a mile.
   - There are 60 minutes in an hour.

   \[
   \text{Speed in mph} = \frac{1463.43 \times 60}{5280} \approx 16.61 \text{ mph}
   \]

So, the bicycle is traveling at approximately 16.6 miles per hour.

Do you want details or have any questions about this solution? Here are some related questions to further your understanding:

1. How would the speed change if the radius of the tire were increased to 15 inches?
2. What would be the bicycle's speed in kilometers per hour?
3. How many revolutions per minute would be required for the bicycle to travel at 20 mph?
4. If the tire's radius was given in centimeters, how would you convert it to inches for this calculation?
5. What is the relationship between tire size and the distance covered in one revolution?

**Tip:** When converting units, always keep track of your conversion factors to ensure accuracy in your calculations.

The tires of a bicycle have radius 13.0 in. and are turning at the rate of 215 revolutions per min. See the figure. How fast is the bicycle traveling in miles per hour? (Hint: 5280 ft = 1 mi)

Learn how to calculate the speed of a bicycle in miles per hour given the tire radius of 13 inches and a rate of 215 revolutions per minute. This problem involves geometry and unit conversion, making it suitable for students in Grades 9-12.

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