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

(1, 30)
left parenthesis 1 comma 30 right parenthesis

(2, 60)
left parenthesis 2 comma 60 right parenthesis

(1 1/2, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis

(15, 1/2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

None of the provided responses represent the correct ratio for the constant of proportionality. The constant of proportionality can be found by dividing the number of pages read by the time taken to read them.

To find the constant of proportionality for Ruth's reading speed, we can divide the number of pages read by the time taken to read them for each data point:

For the first data point: 15 pages / 12 hours = 1.25 pages per hour
For the second data point: 30 pages / 1 hour = 30 pages per hour
For the third data point: 45 pages / 112 hours ≈ 0.4018 pages per hour
For the fourth data point: 60 pages / 2 hours = 30 pages per hour

From these calculations, we can see that the ratio for the constant of proportionality is 30 pages read per hour. Therefore, the correct answer is none of the provided responses.

Answer 2

[AI-generated answer — Explain Bot]

To find the ratio of the constant of proportionality, you can use the formula:

Ratio = Pages read / Time (in hours)

Let's calculate the ratios for each given data point:

1. For the first data point (12 hours, 15 pages):
Ratio = 15 / 12 = 1.25

2. For the second data point (1 hour, 30 pages):
Ratio = 30 / 1 = 30

3. For the third data point (112 hours, 45 pages):
Ratio = 45 / 112 ≈ 0.4018 (rounded to 4 decimal places)

4. For the fourth data point (2 hours, 60 pages):
Ratio = 60 / 2 = 30

Now, let's compare the ratios to find the ratio that remains constant:

- The ratio for the first data point is 1.25
- The ratio for the second data point is 30
- The ratio for the third data point is 0.4018
- The ratio for the fourth data point is 30

From this comparison, we can see that the ratio of the constant of proportionality is 30 (2nd data point: 1 hour, 30 pages). Therefore, the correct answer is (2, 60) or "left parenthesis 2 comma 60 right parenthesis".