To calculate Yu Yan's average swimming speed in miles per minute, we use the formula for speed:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

• The distance she swam is $0.5$ miles.
• The time she took to complete the swim is $25$ minutes.

Thus, her average swimming speed is:

$\text{Speed} = \frac{0.5 \text{ miles}}{25 \text{ minutes}} = 0.02 \text{ miles per minute}$

Yu Yan's average swimming speed is 0.02 miles per minute.

Do you want more details or have any questions?

Here are five related questions you could explore:

1. What is Yu Yan's swimming speed in miles per hour?
2. How long would it take Yu Yan to swim 1 mile at this average speed?
3. If she improved her swim time by 5 minutes, what would her new average speed be?
4. What is the total distance of the triathlon in kilometers?
5. How does her swimming speed compare to her running speed if she runs at 0.1 miles per minute?

Tip: Always ensure your units are consistent when calculating speeds or rates!