JUST KNOW MOST OF THESE ARE FRACTIONS Use the table to answer the question.

Question

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

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

(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

(1, 30)

Answer 1

To find the constant of proportionality, we need to express the relationship between the time spent reading and the number of pages read as a ratio.

Ruth reads 15 pages in 30 minutes, which is 0.5 hours. It means that in 0.5 hours, she reads 15 pages. To find the ratio (constant of proportionality), we will simplify this.

The constant of proportionality \( k \) can be calculated using the formula:

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

Using her reading rate:

\[ k = \frac{15 \text{ pages}}{0.5 \text{ hours}} = 30 \text{ pages per hour} \]

Now looking at the options provided:

1. (15, 12) - This does not represent the constant of proportionality.
2. (15, 1/2) - This also does not represent the correct constant of proportionality.
3. (112, 30) - This does not represent the constant of proportionality.
4. (2, 60) - Here, if we calculate \( \frac{60 \text{ pages}}{2 \text{ hours}} = 30 \) pages per hour. This works for the constant of proportionality.
5. (1, 30) - This ratio does not depict the proportionality constant correctly either as it is numeric for time, not in the context of page reading.

Among those options, (2, 60) reflects the constant of proportionality, which is indeed 30 pages per hour.

Thus, the correct answer is: (2, 60)