Question

The distance John ran is directly proportional to his time in minutes. Consider the table of this relationship.

Time (t) in minutes Distance (d) in miles
62.5 5
125 10
187.5 15


Determine the constant of proportionality.

blank miles per minute

Using the variables for distance (d) and time (t), select the equation to model this situation

d = 12.5t

d = 0.08t

t = 12.5d

t = d + 57.5

Answer 1

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:

1. 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:

2. When \( t = 125 \) minutes, \( d = 10 \) miles:
\[
10 = k \cdot 125
\]
\[
k = \frac{10}{125} = 0.08 \text{ miles per minute}
\]

3. 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.**