To find out how far Jose rode his bicycle, we need to calculate the total distance covered by the wheels. This is done by determining the circumference of the wheel (which is the distance the wheel covers in one full rotation) and then multiplying that by the total number of rotations.

Step 1: Calculate the Circumference of the Wheel

The circumference $C$ of a circle (or wheel in this case) is given by the formula: $C = 2 \times \pi \times r$ where $r$ is the radius of the wheel.

Given:

• Radius $r = 20$ inches

So, $C = 2 \times \pi \times 20 = 40\pi \text{ inches}$

Step 2: Calculate the Total Distance

Now, multiply the circumference by the number of rotations to find the total distance $D$: $D = \text{Circumference} \times \text{Number of Rotations}$ $D = 40\pi \times 5246$ $D = 209840\pi \text{ inches}$

Step 3: Convert Inches to Miles

Since there are 63,360 inches in a mile, we convert the distance to miles: $\text{Distance in miles} = \frac{209840\pi \text{ inches}}{63360 \text{ inches/mile}}$ $\text{Distance in miles} \approx \frac{659599.22}{63360} \approx 10.41 \text{ miles}$

Final Answer:

Jose rode approximately 10.41 miles.

Would you like more details or have any questions about the solution?

Here are some related questions you might find useful:

1. What if the radius of the wheel was 25 inches instead?
2. How would the distance change if the number of rotations was doubled?
3. What is the formula to convert from inches to feet instead of miles?
4. If Jose’s speed was constant, how long did he ride if his speed was 15 miles per hour?
5. How would you calculate the distance if the wheel had a different shape, like an ellipse?

Tip: When dealing with circular motion, always remember that the circumference is the key to finding distances covered with rotations.