Question

It takes John 1/2 hour to walk 2 miles. He at which ratio does the constant of proportionality appear
Table
Hours. Miles
1/4 1
1/2 2
3/4 3
1 4

Answer 1

To find the constant of proportionality (the ratio of miles to hours), we look at the relationship between the two variables: hours and miles.

From the information provided, we can calculate the ratio for each pair of hours and miles:

1. For \( \frac{1}{4} \) hour:
- Distance = 1 mile
- Ratio = \( \frac{1 \text{ mile}}{\frac{1}{4} \text{ hour}} = 4 \text{ miles per hour} \)

2. For \( \frac{1}{2} \) hour:
- Distance = 2 miles
- Ratio = \( \frac{2 \text{ miles}}{\frac{1}{2} \text{ hour}} = 4 \text{ miles per hour} \)

3. For \( \frac{3}{4} \) hour:
- Distance = 3 miles
- Ratio = \( \frac{3 \text{ miles}}{\frac{3}{4} \text{ hour}} = 4 \text{ miles per hour} \)

4. For 1 hour:
- Distance = 4 miles
- Ratio = \( \frac{4 \text{ miles}}{1 \text{ hour}} = 4 \text{ miles per hour} \)

In each case, the ratio of miles walked to hours taken is \( 4 \, \text{miles per hour} \).

Therefore, the constant of proportionality appears as a ratio of 4 miles per hour.