Question

Use the table to answer the question.

Number of Pages Corresponding to the Number of Hours Spent Reading
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

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

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

(1, 30)

Answer 1

To find the constant of proportionality, we need to determine the ratio of pages read to time spent reading. Ruth reads 15 pages in 30 minutes, which is equivalent to 0.5 hours.

So we can calculate the constant of proportionality as follows:

\[
\text{Constant of proportionality} = \frac{\text{Pages read}}{\text{Time in hours}} = \frac{15 \text{ pages}}{0.5 \text{ hours}} = 30 \text{ pages per hour}
\]

Now, looking at the given responses, the correct answer corresponds to the ratio of (1 hour, 30 pages), which is \( (1, 30) \).

This matches with the option:
- **(1, 30)**

Thus, the ratio at which the constant of proportionality is given is \( \text{(1, 30)} \).