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
A. (1,1/4)
B. (4,1)
C.(1/4,1)
D.(1,4)
The constant of proportionality appears when the ratio between the distance and the time is constant. Looking at the data table, we can see that the distance is increasing while the time is constant at 1/2 hour.
The only ratio that remains constant is the ratio between the distance and the time, which is 2 miles / (1/2 hour) = 4 miles/hour.
Therefore, the constant of proportionality appears at ratio (4,1).
The answer is D.(1,4).
In order to determine the ratio at which the constant of proportionality appears in Julian's data table, let's look at the relationship between time and distance.
We know that Julian takes 1/2 hour to walk 2 miles. This means that the ratio of time to distance is 1/2 hour : 2 miles.
Given the answer choices, we can determine the ratio that matches this relationship:
A. (1,1/4): This ratio does not represent the relationship between time and distance as stated in the problem.
B. (4,1): This ratio does not represent the relationship between time and distance as stated in the problem.
C. (1/4,1): This ratio does not represent the relationship between time and distance as stated in the problem.
D. (1,4): This ratio represents the relationship between time and distance. If we multiply 1/2 hour by 4, we get 2 hours, which corresponds to 8 miles. Therefore, the constant of proportionality appears in the ratio (1,4).
Therefore, the correct answer is D. (1,4).
To determine the ratio at which the constant of proportionality appears in Julian's data table, we need to find the relationship between the time it takes for him to walk a certain distance and the distance itself.
We know that it takes Julian 1/2 hour to walk 2 miles. This means that the time and distance have a constant ratio of 1/2 hour to 2 miles. We can write this ratio as:
Time/Distance = 1/2 hour / 2 miles
Simplifying this ratio, we get:
Time/Distance = 1/4 hour/mile
Therefore, the constant of proportionality, which is the ratio between time and distance, appears as 1/4.
Looking at the given answer choices, we can see that the option where the ratio (1/4) appears is:
C. (1/4, 1)
So, the correct answer is C.