Jimmy reads 15 pages in 5 minutes. Carlo reads 12 pages in 6 minutes. Find each constant of proportionality show your work. Then write a sentence to compared the proportional relationship.
To find the constant of proportionality for each person, we'll divide the number of pages read by the time taken.
For Jimmy:
Constant of proportionality for Jimmy = (number of pages read) / (time taken) = 15 / 5 = 3 pages/minute
For Carlo:
Constant of proportionality for Carlo = (number of pages read) / (time taken) = 12 / 6 = 2 pages/minute
Therefore, the constant of proportionality for Jimmy is 3 pages/minute, and for Carlo, it is 2 pages/minute.
Comparing the proportional relationship, we can say that Jimmy reads 1 page more per minute compared to Carlo.
To find the constant of proportionality for Jimmy, we divide the number of pages by the number of minutes: 15 pages / 5 minutes = <<15/5=3>>3 pages/minute.
To find the constant of proportionality for Carlo, we divide the number of pages by the number of minutes: 12 pages / 6 minutes = <<12/6=2>>2 pages/minute.
The proportional relationship for Jimmy can be written as y = 3x, where y is the number of pages read by Jimmy and x is the number of minutes.
The proportional relationship for Carlo can be written as y = 2x, where y is the number of pages read by Carlo and x is the number of minutes.
Both Jimmy and Carlo have a proportional relationship where the number of pages read is directly proportional to the number of minutes. However, the constant of proportionality is different for each person, with Jimmy reading at a rate of 3 pages per minute and Carlo reading at a rate of 2 pages per minute.
To find the constant of proportionality for each person, we divide the number of pages read by the amount of time taken. Let's calculate it step by step:
For Jimmy:
Constant of proportionality = Number of pages read / Time taken
Constant of proportionality = 15 pages / 5 minutes
Constant of proportionality = 3 pages per minute
For Carlo:
Constant of proportionality = Number of pages read / Time taken
Constant of proportionality = 12 pages / 6 minutes
Constant of proportionality = 2 pages per minute
Now, let's compare the proportional relationship between the two:
The constant of proportionality for Jimmy is 3 pages per minute, while the constant of proportionality for Carlo is 2 pages per minute. This means that for every minute, Jimmy reads 3 pages, and Carlo reads 2 pages. Jimmy reads faster than Carlo, as he reads more pages in the same amount of time.