To determine the constant of proportionality and the equation modeling the relationship, we need to understand the relationship between distance \(d\) and time \(t\).
Question 1
Since you mentioned that the distance John ran is directly proportional to his time, we can express this relationship mathematically as:
\[ d = kt \]
where \(k\) is the constant of proportionality (miles per minute).
To find the constant of proportionality, we need data points from the table that show the relationship between distance and time. However, you did not provide the actual values. If you can share the distances and times, we can compute \(k\) as:
\[ k = \frac{d}{t} \]
Question 2
Once we know the constant of proportionality \(k\), we can select the correct equation. In the provided options:
- \(d = 12.5t\)
- \(d = 0.08t\)
- \(t = d + 57.5\)
- \(t = 12.5d\)
If we assume \(k = 12.5\) based on option 1, then that would mean for every minute John runs, he covers 12.5 miles. If \(k = 0.08\), then he covers 0.08 miles per minute.
Based on the question, the correct response depends on the actual constant \(k\) derived from the table's data.
If you provide the values from the table, we can finalize the constant and identify the correct model equation together!