Time (hours) Pages read
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?
(1 point)
Responses
(1, 30)
left parenthesis 1 comma 30 right parenthesis
(2, 60)
left parenthesis 2 comma 60 right parenthesis
(1 1/2, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis
(15, 1/2)
The correct response is (2, 60) because as the time (in hours) doubles from 1 hour to 2 hours, the number of pages read doubles from 30 pages to 60 pages. Therefore, the constant of proportionality is 2:60 or 1:30.
To determine the ratio of the constant of proportionality, we need to look at the relationship between the time (in hours) and the number of pages read.
From the given data, we have:
Time (hours) - Pages Read
1/2 - 15
1 - 30
1 1/2 - 45
2 - 60
To find the constant of proportionality, we need to see how the number of pages read changes as the time increases. Since the data is not in a constant ratio, we can calculate the ratio for each pair of values:
Ratio between 1/2 hour and 15 pages: 15/0.5 = 30
Ratio between 1 hour and 30 pages: 30/1 = 30
Ratio between 1 1/2 hours and 45 pages: 45/(3/2) = 30
Ratio between 2 hours and 60 pages: 60/2 = 30
As we can see, the ratio between the time and the number of pages read is constant at 30. Therefore, the correct response is:
(1, 30)