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?
The constant of proportionality is the ratio of distance to time, or miles walked per hour. From the given table, the ratio of miles walked to hours is constant, as it remains at 4 miles per hour for all values of time. Therefore, the constant of proportionality appears at a ratio of 4:1.
To determine the ratio at which the constant of proportionality appears, we can calculate the miles per hour (the ratio of miles to hours) for each row in the table.
For the given data:
Hours Miles walked Miles per hour
1/4 1 1 / (1/4) = 4
1/2 2 2 / (1/2) = 4
3/4 3 3 / (3/4) = 4
1 4 4 / 1 = 4
As we can see, the ratio of miles per hour is consistently 4 for all the rows in the table. Therefore, the constant of proportionality, in this case, is 4.
To determine the ratio at which the constant of proportionality appears in the given table, we need to find the relationship between the number of hours and the number of miles walked.
In this case, we can observe that as the number of hours Julian walks doubles, the number of miles he walks also doubles. For example, when Julian walks for 1/4 hour, he walks 1 mile, but when he walks for 1/2 hour, he walks 2 miles. This pattern repeats across the other data points in the table as well.
Therefore, the constant of proportionality appears at a ratio of 1:2, indicating that for every 1 hour Julian walks, he walks 2 miles.