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. Make sure to not make it sound like AI.
To find the constant of proportionality for Jimmy, we divide the number of pages he reads (15) by the time it takes him (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 (6 minutes):
Constant of proportionality for Carlo = 12/6 = 2.
The sentence to compare the proportional relationships could be: "For every minute, Jimmy reads 3 pages while Carlo reads 2 pages, showing that Jimmy reads proportionally faster than Carlo."
To find the constant of proportionality, we divide the number of pages by the time it takes to read those pages.
For Jimmy:
Constant of proportionality = 15 pages / 5 minutes
Constant of proportionality = 3 pages per minute
For Carlo:
Constant of proportionality = 12 pages / 6 minutes
Constant of proportionality = 2 pages per minute
Comparing the proportional relationships, we can say that Jimmy can read 3 pages in 1 minute, while Carlo can only read 2 pages in 1 minute. Therefore, Jimmy reads at a faster rate than Carlo.
To find the constant of proportionality for each scenario, we need to calculate the ratio of the number of pages read to the time taken for each person. Let's start with Jimmy.
Jimmy reads 15 pages in 5 minutes, so the constant of proportionality (let's call it k₁) can be found by dividing the number of pages by the time:
k₁ = 15 pages / 5 minutes = 3 pages/minute
Next, let's calculate the constant of proportionality for Carlo.
Carlo reads 12 pages in 6 minutes, so the constant of proportionality for Carlo (let's call it k₂) can be calculated as:
k₂ = 12 pages / 6 minutes = 2 pages/minute
Now, let's compare the two proportional relationships.
The ratio for Jimmy is 3 pages per minute, while for Carlo, the ratio is 2 pages per minute. Therefore, we can conclude that Jimmy reads books at a faster rate than Carlo.
In summary, the constant of proportionality for Jimmy is 3 pages/minute, and for Carlo, it is 2 pages/minute. Comparing the two, Jimmy reads books faster than Carlo.