It takes Julian ¼ 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?

Answer 1

In the given scenario, the time taken by Julian is directly proportional to the distance he walks. To determine the ratio at which the constant of proportionality appears, we need to find the ratio of time to distance.

Given that Julian takes ¼ hour to walk 2 miles, we can create the ratio:

Time : Distance = ¼ hour : 2 miles

Simplifying the ratio by multiplying both the numerator and denominator by 4 gives:

Time : Distance = (¼ hour) * 4 : (2 miles) * 4
= 1 hour : 8 miles

Hence, the ratio at which the constant of proportionality appears is 1 hour : 8 miles.