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?
Responses:
(1, 30)
(15, 1/2)
(1 1/2, 30)
(2, 60)
We can determine the constant of proportionality by calculating the ratio of the number of pages and the corresponding time taken. In this case, Ruth can read 15 pages in 30 minutes, so the ratio would be:
15 pages / 30 minutes = 1/2
Therefore, the correct answer is (15, 1/2).
Determine if the quantities in the data table re in a proportional relationship. If they do not have a proportional relationship, indicate why.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio between the number of pages and the corresponding time taken is the same for all data points.
The data table provided is:
(pages, minutes)
(15, 30)
Since there is only one data point given, we cannot determine if the quantities are in a proportional relationship. We would need more data points to confirm if there is a consistent ratio between the number of pages and the corresponding time taken. Therefore, we cannot determine if the quantities in the data table are in a proportional relationship based on the given information.
To determine the ratio of the constant of proportionality, we can calculate the ratio between the number of pages read and the time taken to read them.
Ruth can read 15 pages in 30 minutes.
This means the ratio is:
15 pages / 30 minutes = 1/2 page per minute
From the options provided, the correct ratio is (15, 1/2).
To find the ratio of the constant of proportionality, we need to analyze the relationship between the number of pages read and the time it takes.
Given that Ruth can read 15 pages in 30 minutes, we can set up a proportion:
15 pages / 30 minutes = x pages / y minutes
To simplify the proportion, we can divide both the numerator and denominator by 15 (the number of pages):
1 page / 2 minutes = x pages / y minutes
Now, we can compare the given options:
Option (1): (1, 30)
To check if this option is the ratio of the constant of proportionality, we substitute the values into the proportion:
1 page / 2 minutes = 1 page / 30 minutes
This option is incorrect because the ratio is not preserved.
Option (2): (15, 1/2)
Substituting the values into the proportion:
1 page / 2 minutes = 15 pages / (1/2) minutes
Simplifying the right side:
1 page / 2 minutes = 15 pages / (1/2) minutes
1 page / 2 minutes = 15 pages / (2/1) minutes
1 page / 2 minutes = 15 pages / 2 minutes
This option is correct because the ratio is preserved. Therefore, the constant of proportionality is 1/2.
Option (3): (1 1/2, 30)
Substituting the values into the proportion:
1 page / 2 minutes = (3/2) pages / 30 minutes
This option is incorrect because the ratio is not preserved.
Option (4): (2, 60)
Substituting the values into the proportion:
1 page / 2 minutes = 2 pages / 60 minutes
This option is incorrect because the ratio is not preserved.
Therefore, the correct answer is option (2), with a ratio of the constant of proportionality as 1/2.