To find the constant of proportionality from the given data, we need to calculate the ratio of pages read to time for the options provided.
First, let's analyze Ruth's initial reading speed:
- Ruth reads 15 pages in 30 minutes. Converting 30 minutes into hours, we have: \[ 30 \text{ minutes} = \frac{30}{60} \text{ hours} = \frac{1}{2} \text{ hours} \] So, her reading speed is: \[ \frac{15 \text{ pages}}{\frac{1}{2} \text{ hours}} = 15 \text{ pages} \times 2 = 30 \text{ pages per hour} \]
Now, let's look at the given data points in the table to determine the consistent ratio of pages read per hour, where the ratio is \( \frac{\text{Pages read}}{\text{Time in hours}} \):
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For \( (12, 15) \): \[ \frac{15 \text{ pages}}{12 \text{ hours}} = \frac{15}{12} = 1.25 \]
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For \( (1, 30) \): \[ \frac{30 \text{ pages}}{1 \text{ hour}} = 30 \]
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For \( (2, 60) \): \[ \frac{60 \text{ pages}}{2 \text{ hours}} = 30 \]
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For \( (112, 45) \): \[ \frac{45 \text{ pages}}{112 \text{ hours}} = \frac{45}{112} \approx 0.40179 \]
From the calculations, the ratio for the reading speed of 30 pages per hour is consistent in options \( (1, 30) \) and \( (2, 60) \).
Therefore, the constant of proportionality at the same reading speed of 30 pages per hour can be represented by the pair \( (1, 30) \) or \( (2, 60) \).
Among the options given, the correct response for the constant of proportionality is \( (1, 30) \).
Thus, the answer is: (1, 30)