Jimmy reads 15 pages in 5 minutes. Caro reads 12 pages in 6 meutes. Find each constant of proportionality, showing your work. Then write a sentence to compare the proportional relationships (2 ports)
Math Short Answer Rubric (2 points)
Paints Awarded
Alors shown
The peston is not and
Complete. But here's the work:
Let's assume the constant of proportionality for Jimmy is represented by k1, and for Caro by k2.
According to the given information, Jimmy reads 15 pages in 5 minutes. So we can write the equation as:
15 = k1 * 5
Simplifying, we have:
k1 = 15/5 = 3
Similarly, for Caro, we have:
12 = k2 * 6
Simplifying, we have:
k2 = 12/6 = 2
So the constant of proportionality for Jimmy is 3, and for Caro is 2.
To compare the proportional relationships, we can say that for every 1 minute, Jimmy reads 3 pages, whereas Caro reads only 2 pages. Therefore, Jimmy's reading speed is faster than Caro's.
To find the constant of proportionality for each situation, we can use the formula k = y/x, where k is the constant of proportionality, y is the dependent variable, and x is the independent variable.
For Jimmy, the dependent variable is the number of pages read (y) and the independent variable is the amount of time in minutes (x). We know that Jimmy reads 15 pages in 5 minutes, so we have:
k = 15/5
k = 3
Therefore, the constant of proportionality for Jimmy is 3.
For Caro, the dependent variable is also the number of pages read (y) and the independent variable is the amount of time in minutes (x). We know that Caro reads 12 pages in 6 minutes, so we have:
k = 12/6
k = 2
Therefore, the constant of proportionality for Caro is 2.
To compare the proportional relationships, we can say that for every 5 minutes, Jimmy reads 15 pages, while for every 6 minutes, Caro reads 12 pages. This implies that Jimmy reads at a faster rate than Caro, since he reads more pages in the same amount of time.
To find the constant of proportionality for each person, we need to divide the number of pages read by the time it took.
For Jimmy:
Number of pages read = 15
Time taken = 5 minutes
Constant of proportionality = Number of pages read / Time taken = 15 / 5 = 3
For Caro:
Number of pages read = 12
Time taken = 6 minutes
Constant of proportionality = Number of pages read / Time taken = 12 / 6 = 2
To compare the proportional relationships:
Jimmy reads 3 pages per minute, while Caro reads 2 pages per minute. Jimmy has a higher constant of proportionality, which means he reads more pages in the same amount of time compared to Caro. Therefore, Jimmy reads faster than Caro.