To determine the constant of proportionality, we can use the relationship that distance \( d \) is directly proportional to time \( t \). This means we can express it using the equation:
\[ d = k \cdot t \]
where \( k \) is the constant of proportionality.
We can find \( k \) using the data provided in the table. Let's use the first entry:
- When \( t = 62.5 \) minutes, \( d = 5 \) miles: \[ 5 = k \cdot 62.5 \] \[ k = \frac{5}{62.5} = 0.08 \text{ miles per minute} \]
Now let's check the other entries to confirm that the constant \( k \) is consistent throughout:
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When \( t = 125 \) minutes, \( d = 10 \) miles: \[ 10 = k \cdot 125 \] \[ k = \frac{10}{125} = 0.08 \text{ miles per minute} \]
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When \( t = 187.5 \) minutes, \( d = 15 \) miles: \[ 15 = k \cdot 187.5 \] \[ k = \frac{15}{187.5} = 0.08 \text{ miles per minute} \]
Since all calculations yield the same result, we confirm that the constant of proportionality \( k \) is:
0.08 miles per minute.
For the equation to model this situation, we can use the form \( d = k \cdot t \).
Given that \( k = 0.08 \), we rewrite the equation:
\[ d = 0.08t \]
Among the provided options, the correct equation to model this situation is:
d = 0.08t.
1 answer