Chaquille can run 3 miles in 22.5 minutes. The direct variation equation y=7.5x gives the relationship between y, the number of minutes Chaquille spends running and x the number of miles he runs.What is the constant of proportionality? What does it represent?
A. The constant of proportionality is 3. This is how many miles Chaquille can run per day
B. The constant of proportionality is 22.5. This is how many minutes Chaquille spends running each day.
C. The constant of proportionality is 7.5. Chaquille runs 7.5 miles per hour
D. The constant of proportionality is 7.5. Chaquille runs each mile in 7.5 minutes
D. The constant of proportionality is 7.5. Chaquille runs each mile in 7.5 minutes.
The correct answer is D. The constant of proportionality is 7.5. It represents the number of minutes Chaquille spends running for each mile he runs.
To find the constant of proportionality, we can compare the values from the given information. The direct variation equation y = 7.5x represents the relationship between the number of minutes Chaquille spends running (y) and the number of miles he runs (x).
From the given information, it is stated that Chaquille can run 3 miles in 22.5 minutes. Let's check if this satisfies the equation y = 7.5x:
y = 7.5x
22.5 = 7.5 * 3
So, the given information satisfies the equation, confirming that the constant of proportionality is indeed 7.5.
Now, let's see what the constant of proportionality represents. In this case, the constant of proportionality, 7.5, represents how many minutes Chaquille spends running per mile. This means that it takes Chaquille approximately 7.5 minutes to run each mile.
Therefore, the correct answer is D. The constant of proportionality is 7.5, and it represents that Chaquille runs each mile in 7.5 minutes.