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 short sentence to compare the proportional relationships.
To find the constant of proportionality for Jimmy's reading rate, we divide the number of pages he reads (15) by the amount of time it takes him to read (5). Therefore, the constant of proportionality for Jimmy is 15/5 = 3 pages per minute.
To find the constant of proportionality for Carlo's reading rate, we divide the number of pages he reads (12) by the amount of time it takes him to read (6). Therefore, the constant of proportionality for Carlo is 12/6 = 2 pages per minute.
The proportional relationship for Jimmy is 3 pages per minute and for Carlo is 2 pages per minute. Jimmy's reading rate is faster than Carlo'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, he reads 15 pages in 5 minutes, so k = 15/5 = 3.
For Carlo, he reads 12 pages in 6 minutes, so k = 12/6 = 2.
To compare the proportional relationships, we can say that for every 1 minute, Jimmy reads 3 pages, while Carlo reads 2 pages. Therefore, Jimmy reads at a faster rate than Carlo.
To find the constant of proportionality for each person, we can divide the number of pages they read by the number of minutes it took.
For Jimmy:
Constant of proportionality = (number of pages)/(number of minutes) = 15/5 = 3
For Carlo:
Constant of proportionality = (number of pages)/(number of minutes) = 12/6 = 2
The constant of proportionality for Jimmy is 3, and for Carlo is 2.
Comparing the proportional relationships, we can say that Jimmy reads 3 pages per minute, while Carlo reads 2 pages per minute. Therefore, we can conclude that Jimmy reads at a faster rate than Carlo.