Use the table to answer the question.
Time(Hours) / Pages Read
T:1/2 PR:15
T:1 PR:30
T:1 1/2 PR:45
T:2 PR:60
Ruth can read 15 pages in 30 minutes. she decides to create a table to keep track of her progress. from a data provided, at what ratio is the constant of proportionality
A (1 1/2, 30)
B (1, 30)
C (15, 1/2)
D (p2, 60)
To find the ratio of the constant of proportionality, we need to determine the relationship between time and pages read. Looking at the table, we can see that as time increases, the pages read also increase. Therefore, the constant of proportionality is the ratio of "Pages Read" to "Time(Hours)".
From the data provided, the ratio of the constant of proportionality is (Pages Read / Time(Hours)):
For the first row: 15 / (1/2) = 30
For the second row: 30 / 1 = 30
For the third row: 45 / (3/2) = 30
For the fourth row: 60 / 2 = 30
Therefore, the ratio of the constant of proportionality is 30.
The correct option is B (1, 30).
To find the constant of proportionality, we need to determine the ratio between the time and the pages read in each row of the table.
In the first row, the time is 1/2 hour and the pages read is 15. The ratio is calculated as:
15 / (1/2) = 15 * 2/1 = 30
In the second row, the time is 1 hour and the pages read is 30. The ratio is calculated as:
30 / 1 = 30
In the third row, the time is 1 1/2 hours and the pages read is 45. The ratio is calculated as:
45 / (3/2) = 45 * 2/3 = 30
In the fourth row, the time is 2 hours and the pages read is 60. The ratio is calculated as:
60 / 2 = 30
From the given data, we can observe that in all four rows, the ratio between time and pages read is always 30. Therefore, the constant of proportionality is 30.
The correct answer is B (1, 30).
To find the ratio of the constant of proportionality from the given data, we can compare the time it took to read the pages (in hours) with the corresponding number of pages read.
Looking at the data:
Time(Hours) / Pages Read
T:1/2 PR:15
T:1 PR:30
T:1 1/2 PR:45
T:2 PR:60
We can see that as the time increases, the number of pages read also increases. This indicates that the constant of proportionality should be the same for all the pairs in the table.
To find the ratio of the constant of proportionality, we can compare any two pairs of time and pages read. Let's choose the first two pairs, T: 1/2 PR: 15 and T: 1 PR: 30.
The ratio of the constant of proportionality can be found by dividing the number of pages read by the corresponding time taken. Let's calculate it for the first pair:
(15 pages) / (1/2 hour) = 30 pages/hour
Now let's calculate it for the second pair:
(30 pages) / (1 hour) = 30 pages/hour
We can see that the ratio is the same for both pairs, and it is equal to 30 pages per hour.
Comparing this with the given answer choices:
A (1 1/2, 30)
B (1, 30)
C (15, 1/2)
D (p2, 60)
We can see that the ratio of 30 pages per hour is not listed in any of the answer choices. Therefore, none of the answer choices represent the correct ratio of the constant of proportionality based on the given data.