Give me a read 15 pages in five minutes. Carla reads 12 pages in six minutes. Find each concept of proportionality showing your work, then write a sentence to compare the proportional relationships.
Let's find the proportional relationship for each person:
For Carla:
Carla reads 12 pages in 6 minutes.
So, her rate of reading is 12 pages / 6 minutes = 2 pages/minute.
For the other person:
The other person reads 15 pages in 5 minutes.
So, their rate of reading is 15 pages / 5 minutes = 3 pages/minute.
To compare the proportional relationships:
The rate of the other person (3 pages/minute) is greater than Carla's rate (2 pages/minute). This means that the other person reads at a faster pace than Carla.
To find the concept of proportionality in this scenario, we can use the formula:
constant of proportionality = (y2 - y1) / (x2 - x1)
Here, let's assign the variables as follows:
x1 = time taken by Carla = 6 minutes
y1 = pages read by Carla = 12 pages
x2 = time taken by you = 5 minutes
y2 = pages read by you = 15 pages
Now, let's calculate the constant of proportionality using the formula:
constant of proportionality = (15 - 12) / (5 - 6)
= 3 / (-1)
= -3
Thus, the concept of proportionality is -3.
To compare the proportional relationships:
The proportional relationship for Carla is that she reads 12 pages in 6 minutes. While for you, the proportional relationship is that you read 15 pages in 5 minutes. Comparing the two, it can be observed that you read more pages in less time compared to Carla.
To solve this problem, we need to find the concept of proportionality between the number of pages read and the time taken for both Carla and the unknown reader.
Let's start with Carla.
Concept of Proportionality for Carla:
We are given that Carla reads 12 pages in 6 minutes. To find the proportionality, we can set up a relationship between the number of pages and the time.
Pages (P) vs. Time (T)
12 pages / 6 minutes
Simplifying the ratio, we find:
P / T = 12 / 6
Simplifying further gives us:
P / T = 2
So, in Carla's case, the concept of proportionality is P / T = 2, where P represents the number of pages and T represents the time in minutes.
Now, let's move on to the unknown reader.
Concept of Proportionality for the Unknown Reader:
We are given that the unknown reader reads 15 pages in 5 minutes. Again, we can set up the relationship between the number of pages and the time.
Pages (P) vs. Time (T)
15 pages / 5 minutes
Simplifying the ratio, we have:
P / T = 15 / 5
Simplifying further gives us:
P / T = 3
So, in the case of the unknown reader, the concept of proportionality is P / T = 3, where P represents the number of pages and T represents the time in minutes.
To compare the proportional relationships, we can say that the unknown reader's rate of reading is faster than Carla's rate. This is because the unknown reader reads 15 pages in 5 minutes, while Carla reads 12 pages in 6 minutes. Therefore, the unknown reader reads at a rate of 3 pages per minute, while Carla reads at a slightly slower rate of 2 pages per minute.