To determine the constant of proportionality and the correct equation for the relationship between distance (d) and time (t), let's break this down step by step based on the information provided.
-
Identify the Constant of Proportionality: The statement mentions that the distance John ran is directly proportional to his time in minutes. If we denote the constant of proportionality as \( k \), then the relationship can be articulated as:
\[ d = kt \]
To determine \( k \), we need to look at the values in the table, which aren't provided in your question. However, the two potential options presented suggest possible values for \( k \):
- \( k = 12.5 \) (i.e., \( d = 12.5t \))
- \( k = 0.08 \) (i.e., \( d = 0.08t \))
If, for example, these correspond to time values of 1 minute leading to a distance of 12.5 miles, then the constant of proportionality would be 12.5. Conversely, if for 1 minute he ran 0.08 miles, the constant would be 0.08.
Without seeing the actual table, you would compare the distance to the corresponding time to find this ratio.
-
Select the Equation to Model the Situation: The options provided are:
- \( d = 12.5t \)
- \( d = 0.08t \)
- \( t = d + 57.5 \)
- \( t = 12.5d \)
Since distance is directly proportional to time, the correct equations that model this case should also follow the form \( d = kt\), meaning you would choose either \( d = 12.5t \) or \( d = 0.08t \), depending on which constant of proportionality you found from the data.
Assuming \( k = 12.5 \) based on typical running distances, the best model equation would likely be:
\[ d = 12.5t \]
Overall, to summarize:
- The constant of proportionality \( k \) is either 12.5 or 0.08, depending on the specific distances given in the table.
- The most fitting equation for the situation, if \( k = 12.5 \), would be \( d = 12.5t \). If \( k = 0.08 \), then it would be \( d = 0.08t \).
Please check the actual values from the table to confirm which constant is correct!
1 answer