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 (15, 12) left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis (1, 30) left parenthesis 1 comma 30 right parenthesis Skip to navigation page 14 of 14
The ratio between the time (hours) and the pages read is the constant of proportionality. From the table, we can see that when Ruth reads for 2 hours, she reads 60 pages. Therefore, the ratio of the constant of proportionality is (2, 60).
To find the ratio of the constant of proportionality, we need to identify two points that have a constant ratio between the number of pages read and the time it took to read them.
From the table, we can see that Ruth read 15 pages in 30 minutes and 112 pages in 45 minutes. The ratio of pages read to time taken for both of these points is:
15 pages / 30 minutes = 0.5 pages per minute
112 pages / 45 minutes = 2.48 pages per minute (rounded to two decimal places)
Since the ratio is not the same for these two points, we can conclude that there is no constant ratio or constant of proportionality in the data provided.
To find the constant of proportionality, we can compare the number of pages read to the time it took to read those pages.
Looking at the table, we see that Ruth read 15 pages in 30 minutes. This means that for every 15 pages she reads, it takes her 30 minutes.
So, the ratio of the constant of proportionality is (15, 30) or 15/30, which simplifies to 1/2.
Therefore, the correct answer is (15, 30) left parenthesis 1 comma 2 right parenthesis.