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. (1/4, 1)
B. (1, 4)
C. (1, 1/4)
D. (4, 1)
To determine the ratio at which the constant of proportionality appears, we can use the given information that it takes Julian 1/2 hour to walk 2 miles. The constant of proportionality represents the required time to walk a given distance.
Let's denote the time (in hours) it takes Julian to walk a certain distance as t, and the distance itself as d (in miles). According to the given information, we can set up the following equation: t = k * d, where k is the constant of proportionality.
We are given that it takes Julian 1/2 hour (0.5 hours) to walk 2 miles. Plugging these values into our equation, we get: 0.5 = k * 2.
Solving for k, we find that k = 0.5/2 = 0.25.
Therefore, the constant of proportionality is 0.25.
Looking at the answer choices, we find that the ratio (0.25, 1) appears in choice A.
So, the correct answer is A. (1/4, 1).
To determine the ratio at which the constant of proportionality appears, we need to analyze the relationship between the time taken and the distance covered.
Given that Julian takes 1/2 hour to walk 2 miles, we can set up the proportion:
(time taken) / (distance covered) = (constant of proportionality)
Substituting the values, we have:
(1/2) / 2 = k
Simplifying the equation:
1/4 = k
So, the constant of proportionality is 1/4.
Thus, the correct option is:
C. (1, 1/4)
To determine the ratio at which the constant of proportionality appears in Julian's data table, we need to examine the relationship between time and distance.
Given that Julian takes 1/2 hour to walk 2 miles, we can set up the proportion:
Time/Distance = Constant of Proportionality
Since Julian's time and distance are both given in relation to a half-hour and 2 miles, we can rewrite the proportion as:
(1/2 hour)/(2 miles) = Constant of Proportionality
Simplifying by dividing the numerator and denominator by 1/2, we get:
1 hour/4 miles = Constant of Proportionality
So, the constant of proportionality in Julian's data table is a ratio of 1 hour to 4 miles.
Looking at the given answer choices:
A. (1/4, 1)
B. (1, 4)
C. (1, 1/4)
D. (4, 1)
The correct answer is D. (4, 1), which represents the ratio of 4 miles to 1 hour, matching the constant of proportionality in Julian's data table.