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
A. (15,1/2)
B. (2,60)
C.(1 1/2,30)
D. (1,30)
The constant of proportionality represents the ratio between the number of pages read and the time it takes to read them. In this case, Ruth can read 15 pages in 30 minutes, so the ratio would be:
15 pages / 30 minutes = 1/2 page per minute
Therefore, the correct answer is: A. (15, 1/2)
To find the ratio of the constant of proportionality, we need to identify a relationship between the number of pages read and the time taken.
Given that Ruth can read 15 pages in 30 minutes, we can set up the following proportional relationship:
Pages read : Time taken = 15 : 30
Simplifying this ratio, we divide both sides by the greatest common divisor (GCD) of 15 and 30, which is 15:
Pages read : Time taken = 1 : 2
Therefore, the ratio of the constant of proportionality is (1, 2), which corresponds to option A. (15, 1/2).
To find the constant of proportionality, we can set up a ratio using the given information.
The ratio will involve two quantities - the number of pages read and the time taken. Let's call the number of pages read "P" and the time taken "T".
From the problem, we know that Ruth can read 15 pages in 30 minutes. So, we have:
P/T = 15/30
Simplifying the ratio, we get:
P/T = 1/2
Now, let's compare this ratio to the options given:
A. (15, 1/2): The ratio in this option is different from the one we derived. So, it's not the correct answer.
B. (2, 60): The ratio in this option doesn't match either.
C. (1 1/2, 30): This option seems close, but we need to convert the mixed number, 1 1/2, into an improper fraction. So, 1 1/2 becomes 3/2. Comparing this ratio to our derived ratio, it does not match. So, it is not the correct answer either.
D. (1, 30): This ratio perfectly matches our derived ratio of 1/2, indicating that the constant of proportionality is indeed 1/2.
Therefore, the correct answer is option D, (1, 30), as the constant of proportionality is 1/30.