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, 30)
left parenthesis 1 comma 30 right parenthesis

(15, 12)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction 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

1 answer

To find the constant of proportionality for Ruth's reading progress, we need to look for the pair (Time, Pages read) that reflects her reading rate.

Ruth reads 15 pages in 30 minutes, which is equivalent to reading 30 pages in 1 hour (because 30 minutes is half an hour).

Now, let's calculate the ratio (constant of proportionality) for the available data pairs based on how many pages are read per hour:

  • For (1 hour, 30 pages): Ratio = 30 pages / 1 hour = 30
  • For (2 hours, 60 pages): Ratio = 60 pages / 2 hours = 30
  • For (1.5 hours, 45 pages): Ratio = 45 pages / 1.5 hours = 30

The constant of proportionality is consistently showing a reading rate of 30 pages per hour.

Among the options provided:

  • (1, 30) - represents reading 30 pages in 1 hour, which is correct and shows the ratio of 30.
  • (2, 60) - represents reading 60 pages in 2 hours, which also shows the ratio of 30.

Therefore, the correct response indicating the constant of proportionality is: (1, 30).