Question

Hi there! Could I have some help solving this Algebra problem?

Your classmate is starting a new fitness program. He is planning to ride his bicycle 60 minutes every day. He burns 7 calories per minute bicycling at 11 mph and 11.75 calories per minute bicycling at 15 mph. How long should he bicycle at each speed to burn 600 calories per hour?

I'm supposed to use a matrix equation to solve it, but I can't figure it out! Any help would be appreciated u w u

Answer 1

do you have your equations set up?

Answer 2

Nope :c That's one of my problems... I can't figure out how to set it up.

Answer 3

how about your variables?

Answer 4

Would the variables be
c=Calories
s=Speed?

Answer 5

not quite

Answer 6

notice how it asks "How long should he bicycle at each speed to burn 600 calories per hour? "

Answer 7

Hmmm... Is it speed and time?

Answer 8

Oh, so it would be speed and calories then?

Answer 9

no

Answer 10

it's actually the two different times for each speed

so you can say something like

x = time devoted to biking at 11 mph
y = time devoted to biking at 15 mph

Answer 11

both times are in minutes

Answer 12

because ultimately we have to answer the question: How long should he bicycle at each speed to burn 600 calories per hour?

Answer 13

the answers will be the values of x and y (actual numbers, not just variables)

Answer 14

Ok, great :) So how would I go about solving this?

Answer 15

before we solve, we need to set up the equations to solve. It's like setting up the question that we have to answer

Answer 16

it says "He is planning to ride his bicycle 60 minutes every day."

so the first equation is x+y = 60

Answer 17

it also adds "He burns 7 calories per minute bicycling at 11 mph and 11.75 calories per minute bicycling at 15 mph"

because he wants to burn 600 calories, this means the second equation is 7x + 11.75y = 600

Answer 18

Hold on, before you go any further, I'm supposed to be using matrices to solve this. Shouldn't I put the x and y values into a variable matrix first?

Answer 19

we'll get there

Answer 20

Wait nvm, I see where you're going with this.

Answer 21

Sorry :P

Answer 22

its ok

Answer 23

we can multiply both sides of 7x + 11.75y = 600 by 100 to get

7x + 11.75y = 600

100*(7x + 11.75y) = 100*600

700x + 1175y = 6000

Answer 24

so we have this system of equations

x+y = 60
700x + 1175y = 6000

how do we turn this into a matrix equation?

Answer 25

oh sorry, typo

Answer 26

700x + 1175y = 6000 should be 700x + 1175y = 60000

forgot a 0

Answer 27

we really have

x+y = 60
700x + 1175y = 60000

Answer 28

Ok, I've got it written down, and I've set up the matrices. What next?

Answer 29

what matrix did you get for the left side?

Answer 30

The coefficient matrix?

Answer 31

yes

Answer 32

Oh, I got [700 1175]

I feel like I'm missing a row...

Answer 33

yes row 1

Answer 34

What should I have entered for row one then?

Answer 35

1 and 1 (the coefficients for x+y)

Answer 36

Ok, that's what I thought :)

Answer 37

your 2x2 matrix should be this