To determine the constant of proportionality from the table, we can analyze the relationship between the time (in hours) and the pages read.
From the data provided:
- At \( \frac{1}{2} \) hour, she reads 15 pages.
- At 1 hour, she reads 30 pages.
- At \( \frac{3}{2} \) hours (1.5), she reads 45 pages.
- At 2 hours, she reads 60 pages.
Now, let's calculate the ratio of pages read to time in hours:
-
For \( \frac{1}{2} \) hour:
\[ \text{Ratio} = \frac{15 \text{ pages}}{\frac{1}{2} \text{ hour}} = 30 \text{ pages per hour} \] -
For 1 hour:
\[ \text{Ratio} = \frac{30 \text{ pages}}{1 \text{ hour}} = 30 \text{ pages per hour} \] -
For \( \frac{3}{2} \) hours:
\[ \text{Ratio} = \frac{45 \text{ pages}}{\frac{3}{2} \text{ hours}} = 30 \text{ pages per hour} \] -
For 2 hours:
\[ \text{Ratio} = \frac{60 \text{ pages}}{2 \text{ hours}} = 30 \text{ pages per hour} \]
In every case, we see that the ratio of pages read to time is consistently 30 pages per hour. Thus, the constant of proportionality is 30.
To answer your question about the ratios given in the options:
- A) \( (15, \frac{1}{2}) = 30 \)
- B) \( (30, 1) = 30 \)
- C) \( (2, 60) = \frac{60}{2} = 30 \)
- D) \( (1 \frac{1}{2}, 30) = \frac{30}{1.5} = 20 \)
The constant of proportionality matches options A, B, and C, but we specifically seek the hour-page relationship, which is best represented by option B (30 pages at 1 hour).
Thus, the answer is B) 1, 30 (interpreting it as the time of 1 hour and the pages read of 30).