Question

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.


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Answer 1

To find the constant of proportionality for both Jimmy and Carlo, we will calculate the pages read per minute for each person.

For Jimmy:

• Pages read: 15 pages
• Time: 5 minutes

To find the constant of proportionality (which is the number of pages read per minute), we divide the number of pages by the time taken:

\[ \text{Constant of proportionality for Jimmy} = \frac{\text{Pages}}{\text{Time}} = \frac{15 \text{ pages}}{5 \text{ minutes}} = 3 \text{ pages per minute} \]

For Carlo:

• Pages read: 12 pages
• Time: 6 minutes

Now, we calculate Carlo's constant of proportionality in the same way:

\[ \text{Constant of proportionality for Carlo} = \frac{\text{Pages}}{\text{Time}} = \frac{12 \text{ pages}}{6 \text{ minutes}} = 2 \text{ pages per minute} \]

Summary of Results:

• Jimmy's constant of proportionality: 3 pages per minute
• Carlo's constant of proportionality: 2 pages per minute

Comparison Sentence:

Jimmy reads faster than Carlo, with a reading rate of 3 pages per minute compared to Carlo's rate of 2 pages per minute.