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Let's break down this problem step by step to determine the expression representing Nikita's distance for the second part of the race.

### Information given:
- Nikita ran a **5-kilometer** race in **39 minutes** (which is 0.65 hours).
- **Part 1**:
  - Speed: **8.75 km/h**
  - Time: **t hours**
  - Distance = Rate × Time = \( 8.75 \times t \) kilometers
- **Part 2**:
  - Speed: **6 km/h**
  - Time: \( 0.65 - t \) hours (since the total time is 0.65 hours, the time for Part 2 is the remaining time)
  - Distance = Rate × Time = \( 6 \times (0.65 - t) \)

The total distance covered is 5 kilometers:
\[
\text{Distance for Part 1} + \text{Distance for Part 2} = 5 \, \text{km}
\]
So:
\[
8.75t + 6(0.65 - t) = 5
\]

From this, the expression representing the distance for the second part of the race is:
\[
6(0.65 - t)
\]

Therefore, the correct answer is the option: 
\[
\boxed{6(0.65 - t)}
\]

Would you like a detailed explanation of the next steps in solving this equation, or do you have any other questions?

### Related Questions:
1. How would you solve the equation to find the value of \( t \)?
2. What would the distance for Part 1 of the race be?
3. How much time did Nikita spend in the second part of the race?
4. What percentage of the total time did Nikita spend running at 6 km/h?
5. How would the expression change if the total time was different?

**Tip**: Always remember that time, rate, and distance are interconnected by the formula \( \text{Distance} = \text{Rate} \times \text{Time} \).

Nikita ran a 5-kilometer race in 39 minutes (0.65 hours) without training beforehand. In the first part of the race, her average speed was 8.75 kilometers per hour. For the second part of the race, her average speed dropped to 6 kilometers per hour. Which expression represents Nikita’s distance for the second part of the race?

Learn how to apply the distance-rate-time relationship to solve a two-part race problem. This example involves a runner covering a 5-kilometer distance with varying speeds in two segments. Includes step-by-step explanation using algebraic expressions. Suitable for middle school students (Grades 6-8).

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