john ran 3 miles in 25.5 minutes.the equation y = 8.5x where x represents the number of miles and y represents the total time in minutes, represents the situation, what is the costant of proportionality represent is this context of the problem?

In the equation \( y = 8.5x \), the constant of proportionality is 8.5. 

### What It Represents:
The constant of proportionality represents the number of minutes John takes to run 1 mile. In other words, John takes 8.5 minutes to run each mile.

### Explanation:
- The equation \( y = 8.5x \) relates the number of miles John runs (denoted by \( x \)) to the total time taken (denoted by \( y \)) in minutes.
- The constant of proportionality (8.5) is the rate at which John runs, in minutes per mile.
- Therefore, in this context, John runs each mile in 8.5 minutes.

Would you like further clarification or additional details?

Here are five related questions you might consider:
1. How long would it take John to run 5 miles?
2. How far can John run in 42.5 minutes?
3. If John wanted to reduce his time per mile to 7 minutes, how would the equation change?
4. How does the constant of proportionality help in comparing different running speeds?
5. What would the equation be if John took 10 minutes per mile instead?

**Tip:** The constant of proportionality provides a useful rate of change in direct variation problems and helps to predict outcomes for different values of the independent variable.

Explore the concept of proportionality in John's running time with the equation y = 8.5x. Learn how the constant of proportionality (8.5) represents the minutes John takes to run each mile. Suitable for students in Grades 7-9 studying direct variation and proportionality in mathematics.

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