To find the constant of proportionality, we can analyze how many pages Ruth reads per hour. The data shows that Ruth reads 30 pages in 1 hour, which is equivalent to 60 minutes, meaning she reads at a rate of 30 pages per hour.
To calculate the constant of proportionality \( k \), we can use the following relation where \( y \) is the number of pages read and \( x \) is the time in hours:
\[ k = \frac{y}{x} \]
Using the provided data points, we can find the constant of proportionality for a few selected pairs:
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For \( (1, 30) \): \[ k = \frac{30}{1} = 30 \]
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For \( (2, 60) \): \[ k = \frac{60}{2} = 30 \]
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For \( (15, 1/2) \): \[ k = \frac{15}{1/2} = 15 \times 2 = 30 \]
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For \( (1 \frac{1}{2}, 45) \) (which is 1.5): \[ k = \frac{45}{1.5} = 30 \]
In all cases, the constant of proportionality \( k \) is consistent and equals 30 pages per hour.
Thus, the ratio for the constant of proportionality for the given data is \( 30 \) pages per hour.
Therefore, the answer that represents this is:
- Ratio for (1, 30) is correct where \( k = 30 \).
So, the constant of proportionality is confirmed at \( 30 \).
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