Time. Pages
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?
A.1:30
B. 15:1/2
C. 1 1/2:30
D. 2:60
To find the ratio of the constant of proportionality, we can divide the number of pages by the time it takes to read them. Let's calculate the ratio for each given time-page combination:
For 1/2 hour to read 15 pages: 15 pages / 30 minutes = 1/2 page per minute
For 1 hour to read 30 pages: 30 pages / 60 minutes = 1/2 page per minute
For 1 1/2 hours to read 45 pages: 45 pages / 90 minutes = 1/2 page per minute
For 2 hours to read 60 pages: 60 pages / 120 minutes = 1/2 page per minute
In all cases, the ratio of pages to time is 1/2 page per minute. Therefore, the ratio of the constant of proportionality is A. 1:30.
To find the ratio of the constant of proportionality, we need to divide the number of pages by the corresponding time for each measurement. Let's calculate the ratios:
For the first measurement:
Ratio = 15 pages / (1/2) time = 15 / (1/2) = 15 * 2 = 30
For the second measurement:
Ratio = 30 pages / 1 time = 30 / 1 = 30 * 1 = 30
For the third measurement:
Ratio = 45 pages / (1 1/2) time = 45 / (1 1/2) = 45 / (3/2) = 45 * 2/3 = 30
For the fourth measurement:
Ratio = 60 pages / 2 time = 60 / 2 = 30
Since the ratios for all the measurements are equal to 30, the constant of proportionality is 30. Therefore, the correct answer is:
A. 1:30
To find the constant of proportionality, we need to determine the relationship between time and the number of pages read. We can do this by dividing the number of pages read by the corresponding time taken for each entry in the table.
Let's calculate the ratios for each entry:
For the first entry: 15 pages / 30 minutes = 1/2
For the second entry: 30 pages / 60 minutes = 1/2
For the third entry: 45 pages / 90 minutes = 1/2
For the fourth entry: 60 pages / 120 minutes = 1/2
As we can see, the ratio between the number of pages read and the time taken is consistently 1/2 for each entry.
Therefore, the constant of proportionality in this case is 1:2, which means for every 1 page read, it takes 2 minutes.
The correct answer choice that represents this ratio is:
D. 2:60