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Use the table to answer the question.

Time (hours) Pages read
1/2 15
1 30
1 1/2 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

(1, 30)

(1 1/2, 30)

(2, 60)

(15, 1/2)

1 answer

To determine the constant of proportionality from the table provided, we look at the ratio of pages read to time in hours.

Based on the data:

  • At 1/2 hour (30 minutes), Ruth reads 15 pages.
  • At 1 hour, she reads 30 pages.
  • At 1 1/2 hours, she reads 45 pages.
  • At 2 hours, she reads 60 pages.

The relationship between pages read and time in hours can be expressed as:

  • For 1/2 hour: \( \frac{15 \text{ pages}}{1/2 \text{ hour}} = 30 \text{ pages per hour} \)
  • For 1 hour: \( \frac{30 \text{ pages}}{1 \text{ hour}} = 30 \text{ pages per hour} \)
  • For 1 1/2 hours: \( \frac{45 \text{ pages}}{1.5 \text{ hours}} = 30 \text{ pages per hour} \)
  • For 2 hours: \( \frac{60 \text{ pages}}{2 \text{ hours}} = 30 \text{ pages per hour} \)

The constant of proportionality is 30 pages per hour, which corresponds to a ratio of (1, 30) since for every 1 hour, she reads 30 pages.

Thus, the correct response is:

(1, 30)