Question

Jimmy reads 15 pages in 5 minutes. Carlo reads 12 pages in 6 minutes. Find each constant of proportionality, showing your work. Then write a sentence to compare the proportional relationships.(2 points)

Math Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.

The answer shows that the student used problem-solving skills and reasoning.

All work is shown or explained.

1
The answer is partially correct. The student made errors while solving.

The answer shows little problem-solving skills or reasoning.

Some work is shown or explained.

0 The question is not answered.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the constant of proportionality for Jimmy, we need to divide the number of pages he reads by the number of minutes it takes him. So Jimmy's constant of proportionality is 15/5 = 3 pages per minute.

To find the constant of proportionality for Carlo, we need to divide the number of pages he reads by the number of minutes it takes him. So Carlo's constant of proportionality is 12/6 = 2 pages per minute.

To compare the proportional relationships, we can say that for every minute, Jimmy reads 3 pages and Carlo reads 2 pages. This means that Jimmy reads faster than Carlo.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the constant of proportionality, we can use the formula k = y/x, where k is the constant of proportionality, x is the independent variable, and y is the dependent variable.

For Jimmy, he reads 15 pages in 5 minutes. So, we can set x = 5 and y = 15. Plugging these values into the formula, we have k = 15/5 = 3.

For Carlo, he reads 12 pages in 6 minutes. Using the same formula, we set x = 6 and y = 12. Plugging these values into the formula, we have k = 12/6 = 2.

To compare the proportional relationships, we can say that for every 5 minutes, Jimmy reads 15 pages, while for every 6 minutes, Carlo reads 12 pages. This means that Jimmy reads at a faster rate than Carlo, since Jimmy reads more pages in less time.

Answer 3

[AI-generated answer — Explain Bot]

To find the constant of proportionality for Jimmy's reading rate, we can use the formula k = y / x, where k is the constant of proportionality, y is the number of pages read, and x is the time taken in minutes.

For Jimmy:
y = 15 pages
x = 5 minutes

k = y / x = 15 / 5 = 3

Therefore, the constant of proportionality for Jimmy's reading rate is 3.

To find the constant of proportionality for Carlo's reading rate, we can use the same formula.

For Carlo:
y = 12 pages
x = 6 minutes

k = y / x = 12 / 6 = 2

Therefore, the constant of proportionality for Carlo's reading rate is 2.

To compare the proportional relationships, we can write a sentence like this:

Carlo's reading rate is proportional to the time he takes to read, with a constant ratio of 2 pages per minute. In comparison, Jimmy's reading rate is also proportional to the time he takes to read, with a constant ratio of 3 pages per minute.

By comparing the constant of proportionality, we can see that Jimmy reads at a faster rate compared to Carlo.