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
To find the constant of proportionality, 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 number of minutes it took.
For Jimmy, we have k₁ = 15/5 = 3.
For Carlo, we have k₂ = 12/6 = 2.
To compare the proportional relationships, we can divide the constant of proportionality for Jimmy by the constant of proportionality for Carlo: k₁/k₂ = 3/2 = 1.5.
This means that for every unit of time, Jimmy reads 1.5 times as many pages as Carlo.
To find the constant of proportionality for Jimmy, we divide the number of pages he read by the time it took him to read them:
Constant of proportionality for Jimmy = 15 pages / 5 minutes = 3 pages/minute
To find the constant of proportionality for Carlo, we divide the number of pages he read by the time it took him to read them:
Constant of proportionality for Carlo = 12 pages / 6 minutes = 2 pages/minute
Therefore, the constant of proportionality for Jimmy is 3 pages/minute, and for Carlo is 2 pages/minute.
To compare the proportional relationships, we can say that Jimmy reads 3 pages every minute, whereas Carlo reads 2 pages every minute. So, Jimmy reads at a faster rate than Carlo.
To find the constant of proportionality for each person, we can divide the number of pages read by the number of minutes it took.
For Jimmy:
Constant of proportionality = Number of pages / Number of minutes
Constant of proportionality = 15 pages / 5 minutes
Constant of proportionality = 3 pages per minute
For Carlo:
Constant of proportionality = Number of pages / Number of minutes
Constant of proportionality = 12 pages / 6 minutes
Constant of proportionality = 2 pages per minute
To compare the proportional relationships, we can write a sentence using the constants of proportionality:
Jimmy reads at a constant rate of 3 pages per minute, while Carlo reads at a constant rate of 2 pages per minute.