Question

Table
Time Pages read
1/2 15
1 30
1 1/2. 45
2 60
Ruth reads 15 pages in 30 minutes at what ratio is the constant of proportionality

Answer 1

To find the constant of proportionality for the relationship between time and pages read by Ruth, we need to determine the ratio of pages read to time.

From the table you provided:

- At 30 minutes, Ruth reads 15 pages.
- The time taken can be expressed in hours or minutes. Since Ruth reads 15 pages in 30 minutes, we can express the constant of proportionality (k) as:

\[
k = \frac{\text{Pages read}}{\text{Time}}
\]

Converting 30 minutes to hours for a clearer proportionality (since common ratios are often expressed per hour):

\[
30 \text{ minutes} = \frac{30}{60} = \frac{1}{2} \text{ hours}
\]

Now calculate the constant of proportionality:

\[
k = \frac{15 \text{ pages}}{\frac{1}{2} \text{ hours}} = 15 \times 2 = 30 \text{ pages per hour}
\]

Thus, the constant of proportionality (ratio of pages read to time) is **30 pages per hour**.