A ferris wheel is a circle with diameter 134 feet which sits on an 8-foot-tall platform making its overall height 142 feet. It completes two revolutions in 2 minutes and 38 seconds. Assuming the riders are at the edge of the circle, how fast are they traveling in miles per hour? (Round your answer to two decimal places.)

To determine the speed of the riders on the ferris wheel, we need to follow these steps:

### Step 1: Calculate the Circumference of the Ferris Wheel
The diameter of the ferris wheel is 134 feet. The formula for the circumference \( C \) of a circle is:
\[
C = \pi \times \text{diameter}
\]
Thus, the circumference is:
\[
C = \pi \times 134 \approx 421.24 \, \text{feet}
\]

### Step 2: Calculate the Total Distance Traveled in Two Revolutions
Since the ferris wheel completes two full revolutions, the total distance traveled is:
\[
\text{Total Distance} = 2 \times 421.24 = 842.48 \, \text{feet}
\]

### Step 3: Convert the Time into Hours
The time taken for two revolutions is 2 minutes and 38 seconds. Convert this time into hours:
\[
2 \, \text{minutes} = \frac{2}{60} \, \text{hours} = \frac{1}{30} \, \text{hours}
\]
\[
38 \, \text{seconds} = \frac{38}{3600} \, \text{hours} \approx 0.01056 \, \text{hours}
\]
So the total time is:
\[
\text{Total Time} = \frac{1}{30} + 0.01056 \approx 0.04323 \, \text{hours}
\]

### Step 4: Calculate the Speed in Feet per Hour
The speed in feet per hour is the total distance divided by the total time:
\[
\text{Speed (ft/hr)} = \frac{842.48 \, \text{feet}}{0.04323 \, \text{hours}} \approx 19,500.32 \, \text{feet per hour}
\]

### Step 5: Convert the Speed into Miles per Hour
There are 5280 feet in a mile, so:
\[
\text{Speed (mph)} = \frac{19,500.32}{5280} \approx 3.7 \, \text{miles per hour}
\]

### Final Answer:
The speed of the riders is approximately **3.7 miles per hour**.

Would you like a more detailed explanation or have any further questions?

---

1. How does the height of the platform affect the speed of the riders?
2. What is the effect of increasing the number of revolutions on the speed calculation?
3. How can we apply similar calculations to other rotating systems?
4. What is the significance of the radius of the ferris wheel in calculating its speed?
5. How does the time for each revolution influence the result?

**Tip:** Always ensure to convert time to consistent units when calculating speed (e.g., hours for miles per hour).

Learn how to calculate the speed of a ferris wheel's riders. This problem involves a ferris wheel with a 134-foot diameter and an 8-foot platform, completing two revolutions in 2 minutes and 38 seconds. The result shows the riders travel at approximately 3.7 miles per hour.

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