A bike with wheels of radius 11 inches is rotating at 14 mi/h.

How many revolutions per minute do the wheels make? (Round to the nearest tenth)

To find the number of revolutions per minute (RPM) that the bike wheels make, we need to relate the speed of the bike to the circumference of the wheels.

### Steps:
1. **Find the circumference of the wheels:**  
   The circumference of a circle is given by:
   \[
   C = 2\pi r
   \]
   where \( r \) is the radius of the wheels.

2. **Convert the bike's speed from miles per hour to inches per minute:**
   - Convert miles per hour to inches per minute using these conversions:
     \[
     1 \text{ mile} = 63,360 \text{ inches}, \quad 1 \text{ hour} = 60 \text{ minutes}
     \]

3. **Determine the revolutions per minute (RPM):**  
   The number of revolutions per minute is the total distance the bike travels in one minute divided by the circumference of the wheel.

Let's calculate it step by step.# Given values
radius_in_inches = 11  # in inches
speed_mph = 14  # miles per hour

# Step 1: Calculate the circumference of the wheel
circumference = 2 * math.pi * radius_in_inches  # in inches

# Step 2: Convert speed from miles per hour to inches per minute
inches_per_mile = 63360  # conversion factor from miles to inches
speed_in_inches_per_minute = (speed_mph * inches_per_mile) / 60  # convert mph to inches per minute

# Step 3: Calculate the revolutions per minute (RPM)
rpm = speed_in_inches_per_minute / circumference

# Round to the nearest tenth
rpm_rounded = round(rpm, 1)
rpm_roundedThe wheels of the bike make approximately **213.9 revolutions per minute** (RPM), rounded to the nearest tenth.

Would you like more details or have any questions? Here are five related questions to expand your understanding:

1. How would the RPM change if the radius of the wheels doubled?
2. What happens to the RPM if the bike's speed increases to 20 mi/h?
3. How do you convert RPM back to the speed in miles per hour?
4. What is the significance of the wheel's radius in determining the RPM?
5. How would you calculate the angular velocity of the wheels in radians per second?

**Tip:** Always ensure units are consistent when converting between speeds, distances, and rotations.

Learn how to calculate the revolutions per minute (RPM) of a bike's wheels with a radius of 11 inches moving at 14 miles per hour. This problem involves geometry, trigonometry, and unit conversions. Understand how to convert speeds from miles per hour to inches per minute and calculate RPM using the circumference formula. Suitable for students in Grades 7-9.

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