Question

Question

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

(112, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis

(2, 60)
left parenthesis 2 comma 60 right parenthesis
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Answer 1

To determine the constant of proportionality from the data provided, we need to find the ratio of pages read to time in hours for each entry in the table. Ruth can read 15 pages in 30 minutes, which means she reads 30 pages in 1 hour. Thus, we can use this information to establish the relationship.

Let's find the ratio (constant of proportionality) for the provided entries by calculating the pages read per hour (pph).

1. For (12 hours, 15 pages):

   • Ratio = 15 pages / 12 hours = 1.25 pages per hour.

2. For (1 hour, 30 pages):

   • Ratio = 30 pages / 1 hour = 30 pages per hour.

3. For (112 hours, 45 pages):

   • Ratio = 45 pages / 112 hours = 0.40179 pages per hour (approximately).

4. For (2 hours, 60 pages):

   • Ratio = 60 pages / 2 hours = 30 pages per hour.

The constant of proportionality provides us with the relationship of how many pages are read per hour. From this, we can see that only the entries for 1 hour (30 pages) and 2 hours (60 pages) stand out with consistent ratios, where both are reading at a speed of 30 pages per hour.

Now, looking at the options provided, the correct answer corresponding to the ratio of pages read to time that maintains consistency is:

(1, 30)

This indicates that for 1 hour, she reads 30 pages, which agrees with her reading speed.

So, the final answer is: (1, 30).