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
(1 1/2, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis
(2, 60)
left parenthesis 2 comma 60 right parenthesis
(1, 30)
left parenthesis 1 comma 30 right parenthesis
(15, 1/2)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis
Skip to navigation
To find the ratio, we need to compare the number of pages read to the corresponding time it took to read them. Looking at the table, it is clear that for every 30 minutes (1/2 hour) Ruth reads 15 pages. This means the ratio of pages read to time is 15:1/2 or 30:1. Therefore, the correct answer is (30, 1/2).
To determine the ratio of the constant of proportionality, we can compare the number of pages read to the corresponding time taken. Looking at the data in the table, we see that when Ruth read for 1 hour, she read 15 pages. Therefore, the ratio of the constant of proportionality is (1, 15). However, none of the given answer choices have this ratio. Therefore, none of the answer choices provided in the question are correct.
To determine the constant of proportionality, we need to find the ratio between the number of pages read and the corresponding time taken in hours.
Looking at the table, we can see that Ruth read 15 pages in 12 hours, 30 pages in 1 hour, 45 pages in 1/2 hours (30 minutes), and 60 pages in 2 hours.
To find the ratio, we can divide the number of pages read by the time in hours for each pair of data points:
- For the first data point: 15 pages / 12 hours = 1.25 pages per hour
- For the second data point: 30 pages / 1 hour = 30 pages per hour
- For the third data point: 45 pages / (1/2) hour = 90 pages per hour
- For the fourth data point: 60 pages / 2 hours = 30 pages per hour
As we can see, the ratio that remains constant throughout is 30 pages per hour. Therefore, the constant of proportionality is (1, 30).
So, the answer is (1, 30).