It takes Julian 1/2 hour to walk 2 miles. He decides to start working 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?
Since Julian takes 1/2 hour to walk 2 miles, we can write the data table as:
Time (in hours) | Distance (in miles)
1/2 | 2
To find the ratio for the constant of proportionality, we need to determine the rate at which Julian is walking, which is the distance he walks per hour.
To find this rate, we can divide the distance by the time:
Rate = Distance / Time
In this case, the distance is 2 miles and the time is 1/2 hour. So, the rate is:
Rate = 2 miles / (1/2) hour
To divide by a fraction, we multiply by its reciprocal:
Rate = 2 miles * (2/1 hour)
Simplifying the expression, we get:
Rate = 4 miles/hour
Therefore, the constant of proportionality appears as the ratio of 4 miles per hour.