Question

I have done part of the questions, but I need help with more (Questions below)

Answer 1

Samantha and Jake are training for a marathon. To prepare for this marathon, they have been training and tracking their progress periodically.
In the first week of training, Jake ran an average of 7.75 minutes per mile. In the fourth week of training, he ran an average of 7.00 minutes per mile.
In the first week of training, Samantha ran an average of 8.10 minutes per mile. In the sixth week of training, she ran an average of 6.60 minutes per mile.
Assuming that Jake and Samantha continue to train and improve their times at the same rate, your task is to determine which week they will have the same average minutes per mile. We will assume that the relationship is linear as they will be training for a maximum of 10 weeks. To complete this task follow the steps below:

Answer 2

1. Determine the equation of the line in standard form that represents Jake’s training progress. His progress corresponds to the points (1, 7.75) and (4, 7.00). You must show all of your work to receive full credit.

My answer was x + 4y = 32, and I'm sure that's right

Answer 3

and then Determine the equation of the line in standard form that represents Samantha’s training progress. Her progress corresponds to the points (1, 8.10) and (6, 6.60). You must show all of your work to receive full credit.
I got 3x + 10y = 84
also sure that it right

Answer 4

Then it says to solve the solution set, and I did this:
x + 4y = 32 --(-10)-->
3x + 10y = 84 -----(4)-->
(-10x – 40y = -320 <--add this
12x + 40y = 336) <---and this
2x = 16
x = 8
-----------------
8 + 4y = 32
4y = 4
y = 1
Solution = (8,1)

Answer 5

I'm not sure If I did that correctly, though

Answer 6

And then it says: In which week will Jake and Samantha have the same average minutes per mile? What will their time be?

This is where I am stuck

Answer 7

Oh, I think I see where I went wrong on #3
I divided instead of subtracted, so I guess it should actually be
8 + 4y = 32
4y = 24
y = 4
Solution = (8,6)?

Answer 8

I meant y = 6

Answer 9

I'm still stuck on
4. In which week will Jake and Samantha have the same average minutes per mile? What will their time be?
though

Answer 10

Oh, I think that the x corresponds to the week and y corresponds to the time?

Answer 11

So..... they will both average 6 minutes in week 8? I think?

Answer 12

Two more questions
5. If Jake and Samantha continue to train until week 33, what will each of their times be?
and
6. Write a paragraph that answers the following questions: Do you believe a linear model best represents the relationship of the time of the runners and the weeks that passed (hint: question 5)? What do you think this says about problems in the real world?