It takes Julian ¼ 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?

Question

It takes Julian ¼ 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?

Answer 1

In the given scenario, the time taken by Julian is directly proportional to the distance he walks. To determine the ratio at which the constant of proportionality appears, we need to find the ratio of time to distance.

Given that Julian takes ¼ hour to walk 2 miles, we can create the ratio:

Time : Distance = ¼ hour : 2 miles

Simplifying the ratio by multiplying both the numerator and denominator by 4 gives:

Time : Distance = (¼ hour) * 4 : (2 miles) * 4
= 1 hour : 8 miles

Hence, the ratio at which the constant of proportionality appears is 1 hour : 8 miles.

Answer 2

To determine the ratio at which the constant of proportionality appears, we need to analyze the given data table and identify any patterns.

According to the information provided, Julian walks 2 miles in ¼ hour. We can create a table to represent this data:

Distance (miles) | Time (hours)
-----------------|-------------
2 | ¼

The ratio between the distance and time is:

2 miles / ¼ hour = 8 miles/hour

So, the constant of proportionality in this case is 8 miles per hour.

Answer 3

To determine the constant of proportionality in this scenario, we need to examine the data table that Julian has created. However, the given information about Julian walking 2 miles in ¼ hour gives us a clue about the proportional relationship.

Let's set up a ratio using the given information:
Distance walked in miles : Time taken in hours
2 miles : ¼ hour

To make the ratio easier to work with, let's convert ¼ hour to a decimal:
¼ hour = 0.25 hour

So the ratio becomes:
2 miles : 0.25 hour

To find the constant of proportionality, we can divide the distance by the time:
2 miles ÷ 0.25 hour = 8 miles/hour

Now we have determined that the constant of proportionality in Julian's case is 8 miles per hour. This means that for every hour Julian walks, he covers a distance of 8 miles.