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 for Jimmy, we divide the number of pages he reads (15) by the time it takes him to read those pages (5 minutes):
Constant of proportionality for Jimmy = 15/5 = 3
To find the constant of proportionality for Carlo, we divide the number of pages he reads (12) by the time it takes him to read those pages (6 minutes):
Constant of proportionality for Carlo = 12/6 = 2
Therefore, the constant of proportionality for Jimmy is 3 and the constant of proportionality for Carlo is 2.
To compare the proportional relationships, we can say that Jimmy reads 3 pages every 1 minute, while Carlo reads 2 pages every 1 minute. This means that Jimmy reads at a faster rate than Carlo.
To find the constant of proportionality for Jimmy, we divide the number of pages he reads (15) by the time it takes him to read those pages (5 minutes):
Constant of proportionality for Jimmy = 15 / 5 = 3
To find the constant of proportionality for Carlo, we divide the number of pages he reads (12) by the time it takes him to read those pages (6 minutes):
Constant of proportionality for Carlo = 12 / 6 = 2
Comparing the two proportional relationships, we can see that for every 5 minutes Jimmy reads 15 pages (constant of proportionality = 3), whereas for every 6 minutes Carlo reads 12 pages (constant of proportionality = 2). Therefore, Jimmy reads at a faster rate than Carlo.
To find the constant of proportionality for each person, we can use the formula:
Constant of Proportionality = (Number of Pages Read) / (Number of Minutes)
For Jimmy, the constant of proportionality can be calculated as:
Constant of Proportionality for Jimmy = 15 pages / 5 minutes = 3 pages per minute
For Carlo, the constant of proportionality can be calculated as:
Constant of Proportionality for Carlo = 12 pages / 6 minutes = 2 pages per minute
Now to compare the proportional relationships, we can say:
Jimmy reads at a rate of 3 pages per minute, while Carlo reads at a rate of 2 pages per minute. This shows that Jimmy reads faster than Carlo.