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)
To find the constant of proportionality, 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 number of pages he reads (y) is the dependent variable and the time it takes (x) is the independent variable.
We have:
k = y/x
k = 15/5
k = 3
For Carlo, the number of pages he reads (y) is the dependent variable and the time it takes (x) is the independent variable.
We have:
k = y/x
k = 12/6
k = 2
Therefore, the constant of proportionality for Jimmy is 3 and for Carlo is 2.
In comparison, Jimmy reads 3 pages for every 1 minute, while Carlo reads 2 pages for every 1 minute. Hence, Jimmy reads at a faster rate than Carlo.