It takes Julian 1/2 hour to walk 2 miles she decides to start walking in her spare time but because she wants to make sure she has enough time to go a desired distance she created the data table what ratio does the constant of proportionality appear? (1,4) (4,1)(1/4,1)(1,1/4)
To determine the constant of proportionality in this scenario, we need to find the ratio between the time taken and the distance traveled.
Given that Julian takes 1/2 hour to walk 2 miles, we can write this as a ratio: 1/2 hour : 2 miles.
Simplifying this ratio, we can multiply both values by 2 to obtain: 1 hour : 4 miles.
Therefore, the constant of proportionality appears in the ratio (1, 4).
To determine the ratio of the constant of proportionality, let's analyze the data table. The data table shows different combinations of time and distance. The first number in each pair represents the time taken, and the second number represents the distance covered.
Given the information that Julian takes 1/2 hour to walk 2 miles, we can conclude that the constant of proportionality is 2 miles divided by 1/2 hour, or 4 miles per hour. This means that for every 1 hour Julian walks, she can cover 4 miles.
Now let's look at the data table:
(1,4): This pair represents 1 hour of walking time and 4 miles of distance covered. This pair matches the ratio we calculated, 4 miles per hour.
(4,1): This pair represents 4 hours of walking time and 1 mile of distance covered. This pair does not match the constant of proportionality since it is the reciprocal of the correct ratio, 1 mile per 4 hours.
(1/4,1): This pair represents 1/4 hour (15 minutes) of walking time and 1 mile of distance covered. This pair does not match the constant of proportionality since it is 1/4 of the correct ratio, 1 mile per 4 hours.
(1,1/4): This pair represents 1 hour of walking time and 1/4 mile of distance covered. This pair does not match the constant of proportionality since it is 1/4 of the correct ratio, 1 mile per 4 hours.
Therefore, the ratio of the constant of proportionality appears in the pair (1,4) in the data table. The constant of proportionality is 4 miles per hour.
To determine the ratio of the constant of proportionality in the given data table, we need to find the ratio of the distances to the corresponding times.
Let's calculate the ratios for each set of data:
1. (1,4):
Distance = 1 mile
Time = 4 hours
Ratio = Distance / Time = 1 / 4 = 1/4
2. (4,1):
Distance = 4 miles
Time = 1 hour
Ratio = Distance / Time = 4 / 1 = 4
3. (1/4,1):
Distance = 1/4 mile
Time = 1 hour
Ratio = Distance / Time = 1/4 / 1 = 1/4
4. (1,1/4):
Distance = 1 mile
Time = 1/4 hour
Ratio = Distance / Time = 1 / (1/4) = 4
From the calculations above, we can see that the ratio of the constant of proportionality appears as 1/4 for the data table (1,4).