To find the constant of proportionality in Julian's data table, we need to look at the relationship between the hours he walked and the miles he covered.
From the given data:
- 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 express this relationship as a ratio of miles walked per hour.
For each entry:
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For 1/4 hour: \[ \frac{1 \text{ mile}}{1/4 \text{ hour}} = 1 \div (1/4) = 4 \text{ miles/hour} \]
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For 1/2 hour: \[ \frac{2 \text{ miles}}{1/2 \text{ hour}} = 2 \div (1/2) = 4 \text{ miles/hour} \]
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For 3/4 hour: \[ \frac{3 \text{ miles}}{3/4 \text{ hour}} = 3 \div (3/4) = 4 \text{ miles/hour} \]
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For 1 hour: \[ \frac{4 \text{ miles}}{1 \text{ hour}} = 4 \text{ miles/hour} \]
In each case, the constant of proportionality (miles per hour) is consistently 4 miles/hour.
Thus, the ratio where the constant of proportionality appears is: \[ \text{Miles walked : Hours walked} = \text{4 miles : 1 hour} \]
The constant of proportionality in this case is \(4\), indicating Julian walks 4 miles for every hour he walks.
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