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To solve this problem of finding the linear velocity of a person riding on a Ferris Wheel, let's break it down step-by-step.

### Given:
- **Diameter of the Ferris Wheel** = 174 feet
- **Time for one complete revolution** = 20 minutes

We are asked to find the **linear velocity** in miles per hour, rounding to the nearest hundredth.

### Step 1: Calculate the Circumference of the Ferris Wheel
The linear velocity depends on the circumference of the Ferris Wheel because one complete revolution means traveling around the circumference.

\[
\text{Circumference} = \pi \times \text{diameter}
\]

Given the diameter is 174 feet:

\[
\text{Circumference} = \pi \times 174 \approx 546.56 \, \text{feet}
\]

### Step 2: Find the Linear Velocity in Feet per Minute
The time for one complete revolution is 20 minutes, so the velocity in feet per minute is:

\[
\text{Velocity (feet per minute)} = \frac{\text{Circumference}}{\text{Time}}
\]

\[
\text{Velocity} = \frac{546.56}{20} \approx 27.33 \, \text{feet per minute}
\]

### Step 3: Convert Feet per Minute to Miles per Hour
To convert feet per minute to miles per hour, we use the following conversion factors:
- 1 mile = 5280 feet
- 1 hour = 60 minutes

So:

\[
\text{Velocity (miles per hour)} = \frac{27.33 \, \text{feet per minute} \times 60 \, \text{minutes}}{5280 \, \text{feet}}
\]

\[
\text{Velocity} = \frac{27.33 \times 60}{5280} \approx 0.31 \, \text{miles per hour}
\]

### Final Answer:
The linear velocity is approximately **0.31 miles per hour**, rounded to the nearest hundredth.

Would you like further details or have any questions?

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Here are 5 related questions to expand your understanding:
1. What is the relationship between angular velocity and linear velocity?
2. How would the velocity change if the Ferris Wheel's diameter increased?
3. How can you convert between angular and linear velocity?
4. What other real-life examples involve calculating linear velocity?
5. How would you solve the same problem if the revolution time was given in seconds?

**Tip:** Always keep conversion factors (like feet to miles, minutes to hours) in mind when dealing with different units in velocity calculations!

A Ferris Wheel has a diameter of 174 feet and one complete revolution takes 20 minutes. Find the linear velocity of a person riding on the wheel. Give your answer in miles per hour and round to the nearest hundredth.

Solve a real-world problem involving a Ferris Wheel with a diameter of 174 feet and a 20-minute revolution. Learn how to calculate the linear velocity of a person riding it in miles per hour, using formulas for circumference and velocity. Suitable for Grades 9-12.

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