Hours. Miles
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 he created the data table. At which ratio does the constant of proportionality appear?
A. 1/4:1
B. 1:1/4
C. 1:4
D. 4:1
The ratio of hours to miles in the data table is consistent. This means that the constant of proportionality appears in the ratio of hours to miles. Looking at the data table, we can see that the constant of proportionality is 1/2 (since it always takes Julian 1/2 hour to walk 2 miles).
To express this ratio, we can write it as 1/2:2 or simplify it to 1:4.
Therefore, the answer is (D) 4:1.
To find the ratio at which the constant of proportionality appears, we need to compare the hours and miles in the data table.
Looking at the table, we can see that for every 1/2 hour, Julian walks 2 miles. This means the ratio of hours to miles is 1/2:2.
To simplify the ratio, we can multiply both the numerator and denominator by 2 to get a whole number:
1/2 * 2 = 1,
2 * 2 = 4.
So the simplified ratio is 1:4.
Therefore, the constant of proportionality appears at a ratio of 1:4.
The answer is (C) 1:4.
To determine the ratio at which the constant of proportionality appears, we need to find the relationship between the hours and the miles.
Looking at the table, we observe that the ratio of miles to hours remains constant, which implies that there is a constant of proportionality between them.
Let's determine the constant of proportionality for each pair of values:
For the first pair (1/4 hour and 1 mile):
To find the constant of proportionality, we can divide the number of miles by the number of hours:
1 mile / (1/4) hour = 4 miles/hour
For the second pair (1/2 hour and 2 miles):
Again, dividing the miles by the hours:
2 miles / (1/2) hour = 4 miles/hour
We can see that both pairs have the same constant of proportionality, which is 4 miles/hour.
Therefore, the correct ratio at which the constant of proportionality appears is D. 4:1.