Time (Hours) pages
1/2 15
1 30
1 1/2 45
2 60
Ruth can read 15 pages in 30 minutes. She decides to create a table to keep track of her progress. From the data provided, what is the constant of proportionality.
A. (2, 60)
B. (1 1/2, 30)
C. (15, 1/2)
D. (1,30)
The constant of proportionality can be found by dividing the number of pages read by the time it took to read them. This will be the same for any of the given data points.
For example, at 1/2 hour, Ruth read 15 pages. The constant of proportionality is therefore 15 divided by 1/2, or 30.
So the correct answer is choice D. (1,30).
To find the constant of proportionality, we need to determine the ratio of the number of pages to the amount of time for each data point.
From the given data, we can determine the different ratios:
- For the first data point, the ratio is 15 pages / (1/2 hours) = 30 pages/hour.
- For the second data point, the ratio is 30 pages / 1 hour = 30 pages/hour.
- For the third data point, the ratio is 45 pages / (1 1/2 hours) = 30 pages/hour.
- For the fourth data point, the ratio is 60 pages / 2 hours = 30 pages/hour.
As we can see, the ratio is constant regardless of the time. The constant of proportionality is the ratio 30 pages/hour.
Hence, the correct answer is:
B. (1 1/2, 30)
To find the constant of proportionality, we need to examine the relationship between the time in hours and the corresponding number of pages that Ruth can read in that time.
Looking at the table, we can see that when the time is doubled, the number of pages is also doubled. For example, when the time is 1 hour, Ruth reads 30 pages, and when the time is 2 hours, she reads 60 pages. This indicates that there is a linear relationship between the time and the pages, and the constant of proportionality is the ratio of the number of pages to the time.
To calculate the constant of proportionality, we can choose any two points from the table. Let's choose the points (1/2 hour, 15 pages) and (2 hours, 60 pages).
The ratio of the number of pages to the time for the first point is 15/1/2 = 30, and for the second point, it is 60/2 = 30.
Therefore, the constant of proportionality is 30.
From the given options, the correct answer is D. (1, 30), where 1 represents the time in hours, and 30 represents the number of pages Ruth can read in that time.