Use the table to answer the question.

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 find the constant of proportionality from the given data, you can determine the ratio of pages read to time (in hours).

From the provided data:

1. (12 hours, 15 pages) → Ratio: \( \frac{15}{12} = \frac{5}{4} \)
2. (1 hour, 30 pages) → Ratio: \( \frac{30}{1} = 30 \)
3. (112 hours, 45 pages) → Ratio: \( \frac{45}{112} \approx 0.4018 \)
4. (2 hours, 60 pages) → Ratio: \( \frac{60}{2} = 30 \)

Now, to find the constant of proportionality for Ruth based on her reading speed of 15 pages in 30 minutes, we first convert 30 minutes to hours: \( 30 \text{ minutes} = 0.5 \text{ hours} \).

So, the ratio for Ruth is:

• (0.5 hours, 15 pages) → Ratio: \( \frac{15}{0.5} = 30 \)

Now, we look for the option which matches a ratio of 30:

• (1, 30)
• (15, 12)
• (112, 30)
• (2, 60)

The pair (2, 60) corresponds to a reading of 60 pages in 2 hours, which simplifies to 30 pages per hour, aligning with our constant of proportionality.

Thus, the answer is: (2, 60).