Use the table to answer the question.
Hours Miles walked
14 1
12 2
34 3
1 4
It takes Julian 12 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 ratio of the number of hours to the number of miles walked is the constant of proportionality in this situation.
To find the ratio at which the constant of proportionality appears, we need to determine if the ratio of the number of hours to the number of miles walked is constant throughout the table.
Let's calculate the ratios for each row:
For the first row (14 hours, 1 mile), the ratio is 14/1 = 14.
For the second row (12 hours, 2 miles), the ratio is 12/2 = 6.
For the third row (34 hours, 3 miles), the ratio is 34/3 ≈ 11.33.
For the fourth row (1 hour, 4 miles), the ratio is 1/4 = 0.25.
Since the ratios are not constant throughout the table, the constant of proportionality does not appear in this set of data.
To determine the ratio at which the constant of proportionality appears in the given data table, we need to compare the hours and miles walked for each entry.
First, we can calculate the ratios for each entry by dividing the number of miles walked by the number of hours taken.
For the given data table:
- For the first entry (14 hours, 1 mile): 1 mile / 14 hours = 1/14
- For the second entry (12 hours, 2 miles): 2 miles / 12 hours = 1/6
- For the third entry (34 hours, 3 miles): 3 miles / 34 hours = 3/34
- For the fourth entry (1 hour, 4 miles): 4 miles / 1 hour = 4/1
Comparing these ratios, we can see that the constant of proportionality appears at the ratio of 1/6. This means that for every 1/6 of an hour (or 10 minutes), Julian walks 1 mile.
Therefore, the constant of proportionality appears at the ratio of 1/6.