To solve the problem, we determine how many minutes the fan rotated using the formula:

$\text{Minutes} = \frac{\text{Total Rotations}}{\text{Rotations per Minute}}$

Given:

• Total Rotations = $3,764.75$
• Rotations per Minute = $150.59$

Now we calculate:

$\text{Minutes} = \frac{3,764.75}{150.59}$

Performing the division:

$\text{Minutes} = 25 \, \text{(approximately, rounded to the nearest whole number)}.$

Thus, the fan rotated for 25 minutes.

The correct answer is: D. The fan rotated for 25 minutes.

Would you like further details on the calculation? Here are some related questions for deeper understanding:

1. How do you calculate the time for non-integer rotations per minute?
2. What happens if the rotations per minute increase by 10%? How does it affect the total time?
3. Can we express the rotations as a percentage of rotations per minute for a fraction of a minute?
4. Why is it important to round appropriately in real-world problems like this one?
5. If the fan rotates 1,000 more times, how much additional time would that add?

Tip: Always check units (e.g., minutes, rotations) to ensure your calculations are correct.