2 law students went out after school to read the pages they were..... the rest of the question is below

Question

2 law students went out after school to read the pages they were assigned in class alejandro can read 1 page per minute,and he read 28 pages. carly has a speed of 2 pages per minute, has read 12 pages so far.

part

A: define the variables and write 2 equations to represent the number of pages that each student read. 

Variables:

Alejandro:

Carly:

part B: what is the rate of change for each student 

Part C: what does the rate of change represent in this situation.

part D: what is the y interccept for carly? what does it represent?

Part G: give an example when alejandro has read more pages than carly. justify your answer

 

Answer 1

Part A)

Let us first begin by understanding what Alejandro can read. We are told that he can read one page in one minute, so his rate or slope is 1pg/1min and we are told that he is starting at page 28 of his book, which is another way of saying that the y-intercept is 28. So, how can we put all of this information into the slope intercept formula (y=mx+b). We know that the number of pages Alejandro can read is dependent on the time that he can read them in, so pages is the y variable and time is the x variable. We can use all of this information to write the following formula

Pa = Ta +28

Now, lets follow the same reasoning to create an equation for Carly. We are told that Carly's rate is 2 pages per minute, or a slope of 2pgs/1min, and that she starts at page 12 of her book, or a y-intercept of 12. We can use this information to write the following formula

Pc = 2Tc +12

Part B)

Based on the above equations the rate of change, or slope, of Alejandro is 1pg/1min and the slope of Carly is 2pgs/1min.

Part C)

The rate of change in these situations represents the slope on a line.

Part D)

The y-intercept for Carly is 12 and it represents that she started reading at page 12.

Part G)

Alejandro has read more pages then Carly from 1 minute into reading to 15 minuets into reading because...

Ta +28 > 2Tc +12

We are going to assume that the times are the same since we are trying to find the maximum amount of time Alejandro can read and still be ahead of Carly. So...

T + 28 > 2T +12

T < 16

So, as long as Alejandro's time is less than 16 minutes, he will be ahead in the book.