Question

Use the table to answer the question.
Hours Miles walked
1/4 1
1/2 2
3/4 3
1 4
It takes Julian 1/2 hour to walk 2 miles. He decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear

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Answer 1

To find the constant of proportionality in the context of Julian's walking distance, we can look at the relationship between the hours he walks and the miles he covers.

From the data provided in the table:

- 1/4 hour corresponds to 1 mile
- 1/2 hour corresponds to 2 miles
- 3/4 hour corresponds to 3 miles
- 1 hour corresponds to 4 miles

We can determine the constant of proportionality (k) by finding the ratio of miles to hours for any entry in the table.

Let's calculate it using the first entry:

For 1/4 hour:
\[
k = \frac{\text{Miles}}{\text{Hours}} = \frac{1 \text{ mile}}{1/4 \text{ hour}} = 4
\]

For 1/2 hour:
\[
k = \frac{2 \text{ miles}}{1/2 \text{ hour}} = 4
\]

For 3/4 hour:
\[
k = \frac{3 \text{ miles}}{3/4 \text{ hour}} = 4
\]

For 1 hour:
\[
k = \frac{4 \text{ miles}}{1 \text{ hour}} = 4
\]

In each case, the constant of proportionality is 4, which indicates that Julian walks 4 miles for every hour he walks. Therefore, the ratio at which the constant of proportionality appears is:

**4 miles per hour**.