Use the table to answer the question.
Time (hours) Pages read
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, at what ratio is the constant of proportionality?
(1 point)
Responses
(15, 1/2)
(1 1/2, 30)
(1, 30)
(2, 60)
The constant of proportionality is found by dividing the number of pages read by the corresponding time in hours.
From the table, we can see that the number of pages read doubles as the time in hours doubles.
Therefore, the constant of proportionality is a ratio of 1.
The correct answer is (1, 30).
To determine the ratio of the constant of proportionality, we need to find the ratio between the number of pages read and the corresponding time in hours.
Let's look at the table provided:
Time (hours) | Pages read
1/2 | 15
1 | 30
1 1/2 | 45
2 | 60
We can see that for every 1-hour increase in time, the number of pages read also increases by 30 pages. Therefore, the ratio of the constant of proportionality is:
(1, 30)
So the correct answer is:
(1, 30)
To find the ratio of the constant of proportionality, we need to determine how the number of pages read changes as the time increases. From the given table:
When the time is 1/2 hour, Ruth reads 15 pages.
When the time is 1 hour, Ruth reads 30 pages.
When the time is 1 1/2 hours, Ruth reads 45 pages.
When the time is 2 hours, Ruth reads 60 pages.
To find the ratio, we need to compare the change in pages read to the change in time. Let's calculate the differences in both for each consecutive pair of data points:
Between (1/2 hour, 1 hour): 30 - 15 = 15 pages; 1 hour - 1/2 hour = 1/2 hour
Between (1 hour, 1 1/2 hours): 45 - 30 = 15 pages; 1 1/2 hours - 1 hour = 1/2 hour
Between (1 1/2 hours, 2 hours): 60 - 45 = 15 pages; 2 hours - 1 1/2 hours = 1/2 hour
Now we can see that the ratio is constant at 15 pages per 1/2 hour. Therefore, the correct answer is (15, 1/2).