Question

I think I've got the answers on my own here but I just want to make sure because when I do math and it's easy, I know I've gotten something wrong. Anyway here are the questions:
1. Determine the equation of a line in standard form that represents Jake’s training progress. His progress corresponds to the points (1, 9.50) and (4, 6.75). The answer I got was 11x+12y=125. ( my teacher wants it in that form)
2. Determine the equation of a line in standard form that represents Samantha’s training progress. Her progress corresponds to the points (1, 8.75) and (5, 5.75). The answer I got was 3x+4y=3

Answer 1

The first one is right.
I got 3x + 4y = 38 for the second

Answer 2

Oh the 8 must've gotten cut off when typed, is it okay if I ask two more questions?

Answer 3

ok

Answer 4

The third question I have is asking me to solve the system of equations for the two problems above and I don't think I got the right answers. My answers are: x=11/12 y=43/8

Answer 5

The reasons I don't think I got the right answers is because the next question after that is asking me At what moment will Jake and Samantha have the same average minutes per mile? I know I have to plug in x and y here

Answer 6

The third one is x = 11/2 and y = 43/8. Was the 11/12 a typo?

The fourth is asking you to interpret what the result from #3.
I'm assuming x is time, and y is the rate. So they would have the same rate at x = 11/2 (not sure what the units are here, minutes hours, or seconds)

Answer 7

nope 11/12 is what I got for x and the units are weeks

Answer 8

does your question say what the units are for y and what it represents?

Answer 9

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 9.50 minutes per mile. Later, in week four of training he ran an average of 6.75 minutes per mile.
In the first week of training Samantha ran an average of 8.75 minutes per mile. Later, in week five of training she ran an average of 5.75 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.

Answer 10

That's all that I was given

Answer 11

you got the y-coordinate right, so substitute it into one of the equations to find x.

3x + 4y = 38
3x + 4(43/8) = 38
3x +43/2 = 38
3x = 38 - 43/2
3x = 33/2
x = 11/2

Answer 12

and I would use the y and x values for #4?

Answer 13

yes. So they would have the same avg time at x = 11/2, which is 5.5 weeks after they start training

Answer 14

Alright thanks for all of your help! :)

Answer 15

you're welcome