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Let's solve the questions based on the provided Ferris wheel information:

1. **Ferris wheel diameter**: 250 feet.
2. **One full revolution**: 10 minutes (600 seconds).

### a. How many degrees would the Ferris wheel rotate in 100 seconds?
- One full revolution equals 360° in 600 seconds.
- The rotation per second is \( \frac{360}{600} = 0.6^\circ \) per second.
- In 100 seconds, the wheel would rotate:
  \[
  0.6^\circ \times 100 = 60^\circ
  \]
  **Answer**: The Ferris wheel would rotate **60 degrees** in 100 seconds.

### b. How far has a person traveled if they have been on the Ferris wheel for 7 minutes?
- The radius of the Ferris wheel is half the diameter, so:
  \[
  r = \frac{250}{2} = 125 \text{ feet}.
  \]
- The circumference of the Ferris wheel is the distance for one full revolution:
  \[
  C = 2\pi r = 2\pi \times 125 \approx 785.4 \text{ feet}.
  \]
- If the person has been on for 7 minutes (420 seconds), they complete:
  \[
  \frac{420}{600} = 0.7 \text{ of a revolution}.
  \]
- The distance traveled is 70% of the total circumference:
  \[
  0.7 \times 785.4 \approx 549.78 \text{ feet}.
  \]
  **Answer**: The person has traveled approximately **549.78 feet** in 7 minutes.

### c. How long would it take for a person to travel 200 feet?
- One full revolution travels 785.4 feet.
- To find how long it takes to travel 200 feet, set up the proportion:
  \[
  \frac{200}{785.4} \approx 0.2547 \text{ of a revolution}.
  \]
- Since one revolution takes 10 minutes (600 seconds), the time is:
  \[
  0.2547 \times 600 \approx 152.82 \text{ seconds}.
  \]
  **Answer**: It would take approximately **152.82 seconds** to travel 200 feet.

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Do you need further details or have any questions? Here are five related questions:

1. What would be the speed of the Ferris wheel in feet per second?
2. How many revolutions would the Ferris wheel complete in one hour?
3. How many degrees would the Ferris wheel rotate in 30 seconds?
4. What is the linear speed of a person at the edge of the Ferris wheel in feet per minute?
5. How far would a person travel if they stayed on the Ferris wheel for one full hour?

**Tip**: Remember that the circumference is directly related to how far you travel in one revolution of a circular object like a Ferris wheel!

The first Ferris wheel had a diameter of 250 feet and took 10 minutes to complete one full revolution. How many degrees would the Ferris wheel rotate in 100 seconds? How far has a person traveled if he or she has been on the Ferris wheel for 7 minutes? How long would it take for a person to travel 200 feet?

Calculate the rotation degrees, distance traveled, and time taken on a Ferris wheel with a 250-feet diameter. Learn step-by-step how to determine the degrees of rotation in 100 seconds, distance traveled in 7 minutes, and time to travel 200 feet.

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