Use the table to answer the question.
Time (hours) Pages read
12 15
1 30
112 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
(2, 60)
left parenthesis 2 comma 60 right parenthesis
(112, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis
(1, 30)
left parenthesis 1 comma 30 right parenthesis
(15, 12)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis
Skip to navigation
The ratio is (1, 30) left parenthesis 1 comma 30 right parenthesis
To determine the constant of proportionality from the table, we need to find a relationship between the time (in hours) and the pages read.
The ratio of Ruth's progress at different times can give us this information. Let's calculate the ratios:
For the first entry: (12 hours, 15 pages read)
Ratio = 15 pages / 12 hours = 1.25 pages/hour
For the second entry: (1 hour, 30 pages read)
Ratio = 30 pages / 1 hour = 30 pages/hour
For the third entry: (1 hour, 45 pages read)
Ratio = 45 pages / 1 hour = 45 pages/hour
For the fourth entry: (2 hours, 60 pages read)
Ratio = 60 pages / 2 hours = 30 pages/hour
Since the ratios are consistent, and the value that repeats is 30 pages/hour, the constant of proportionality is (1, 30). Therefore the correct answer is:
(1, 30)
To determine the ratio that represents the constant of proportionality, we need to look for a relationship between the time and the pages read that remains consistent.
In this table, we can see that as the time increases, the number of pages read also increases. More specifically, the number of pages read doubles as the time doubles.
By comparing the time and the number of pages read, we can see that when the time is 1 hour, Ruth reads 30 pages. This means that the ratio between the time and the number of pages read is 1:30.
Therefore, the correct answer is (1, 30), which represents the ratio for the constant of proportionality in this table.