It takes Julian 1/2

Question

hour to walk 2 miles. He decides to start working 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?

(1 point)
Responses

(14,1)
open paren 1 fourth comma 1 close paren

(12, 2)
(12, 2)

(34, 3)
(34, 3)

(1,4)
open paren 1 comma 4 close paren
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Answer 1

To determine the constant of proportionality in Julian's walking distance, we first need to find his walking speed.

Julian walks 2 miles in 1/2 hour.

To find his speed in miles per hour (mph):

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \text{ miles}}{0.5 \text{ hour}} = 2 \div 0.5 = 4 \text{ mph} \]

Now, the ratio of distance to time can help us find the constant of proportionality:

Distance (miles) : Time (hours) = 2 : 0.5

To express it as a ratio that helps identify the constant of proportionality, we can write:

\[ \frac{\text{Distance}}{\text{Time}} = \frac{2}{0.5} = 4 \]

Thus, for distances covered in different time durations, the ratio will always reflect this constant speed.

Now, looking at the options given:

1. (14,1)
2. (1/4, 1)
3. (12, 2)
4. (34, 3)
5. (1, 4)

Among these, the most relevant option for the constant of proportionality (speed) based on our calculations of distance and time ratios is (1, 4), since it suggests that for every 1 hour he walks, he will cover 4 miles, which matches his speed of 4 mph.

Answer: (1, 4)