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 (2, 60)
To find the constant of proportionality, we need to divide the number of pages by the time it takes to read those pages.
The first data point is given as (1 1/2, 30). This means that Ruth reads 1.5 pages in 30 minutes. The ratio of pages to minutes is 1.5/30 = 0.05.
The second data point is given as (1, 30). This means that Ruth reads 1 page in 30 minutes. The ratio of pages to minutes is 1/30 = 0.0333.
The third data point is given as (15, 1/2). This means that Ruth reads 15 pages in 0.5 minutes. The ratio of pages to minutes is 15/0.5 = 30.
The fourth data point is given as (2, 60). This means that Ruth reads 2 pages in 60 minutes. The ratio of pages to minutes is 2/60 = 0.0333.
Comparing the ratios of pages to minutes, we can see that the correct ratio for the constant of proportionality is:
C. (15, 1/2)
To determine the ratio of the constant of proportionality, we need to find the ratio between the number of pages read and the time it takes to read them.
Given that Ruth can read 15 pages in 30 minutes, the ratio is:
15 pages / 30 minutes
Simplifying this ratio, we get:
1/2 pages per minute
So the correct answer is:
C (15, 1/2)
To find the constant of proportionality, we need to examine the relationship between the number of pages Ruth reads and the time it takes her. We can do this by comparing the values given in each option.
Let's calculate the ratio of the number of pages to the time for each option:
A: 15 pages / 30 minutes = 1/2
B: 1 page / 30 minutes = 1/30
C: 15 pages / 1/2 minute = 30
D: 2 pages / 60 minutes = 1/30
From these calculations, we can see that the ratio of the constant of proportionality corresponds to option C: (15, 1/2). Therefore, the correct answer is C.