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
1. (1,4)
2. (4,1)
3. (1, 1/4)
4. (1/4, 1)
The constant of proportionality appears in the ratio (1/4, 1). Here's why:
In the data table, we have the distance (in miles) Julian walks on the left side and the time (in hours) it takes him on the right side.
From the information given, we know that it takes Julian 1/2 hour to walk 2 miles. To find the constant of proportionality, we divide the distance by the time:
2 miles รท 1/2 hour = 4 miles/hour
So, the constant of proportionality is 4 miles/hour. In a ratio format, this can be expressed as (1/4, 1) because for every 1 hour, Julian walks 4 miles.
The constant of proportionality appears at the ratio of (1/4, 1).
To find the ratio indicating the constant of proportionality in Julian's situation, we need to look for a consistent relationship between the time taken and the distance covered.
From the given information, we know that Julian takes 1/2 hour to walk 2 miles. This can be written as 1/2 : 2, where the time is the numerator and the distance is the denominator.
Now let's check the options to see if any of them share the same ratio.
1. (1,4): The ratio here is 1:4, which is not the same as the original ratio.
2. (4,1): The ratio here is 4:1, which is not the same either.
3. (1, 1/4): This ratio is 1:1/4, which is equivalent to 4:1. This matches the original ratio of 1/2:2.
4. (1/4, 1): The ratio here is 1/4:1, which is the same as 1:4. This is not the correct ratio.
Therefore, the ratio that indicates the constant of proportionality in Julian's situation is option 3: (1, 1/4).