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

(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

(2, 60)

Answer 1

To find the constant of proportionality, we can examine the relationship between the time (in hours) and the pages read.

From the data you provided:

1. When time \( t = 1 \) hour, pages read = 30 pages.
2. When time \( t = 2 \) hours, pages read = 60 pages.

The constant of proportionality \( k \) can be found using the formula:

\[ k = \frac{\text{pages read}}{\text{time}} \]

Using the values given:

1. For \( t = 1 \) hour: \[ k = \frac{30 \text{ pages}}{1 \text{ hour}} = 30 \text{ pages/hour} \]

2. For \( t = 2 \) hours: \[ k = \frac{60 \text{ pages}}{2 \text{ hours}} = 30 \text{ pages/hour} \]

Thus, the constant of proportionality is 30 pages per hour.

Looking at the options:

• \( (1, 30) \) corresponds to 1 hour reading 30 pages, which is the proper representation of the constant of proportionality.

So the answer is: (1, 30).