Question

LAST JUAN!

Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jennifer to complete this job on her own.

Answer 1

@Hero e.e

Answer 2

Use the formula

Answer 3

I know you have the formula. I gave it to you. So at least write that out first.

Answer 4

ok hold on

Answer 5

\[t=\frac{ CJ }{ C+J }\]

Answer 6

Okay wait.

Answer 7

e.e

Answer 8

This is a bit more involved than you think. The only given value is \(t\)

Answer 9

It says Carl can paint a room 3 hours faster than Jennifer can. So we don't have any given values for \(C\) or \(J\)

Answer 10

ok

Answer 11

However we can create a statement based on this:
"Carl can paint a room 3 hours faster than Jennifer".

Answer 12

It translates to
\(C = J + 3\)

Answer 13

ok

Answer 14

In other words we insert \(J + 3\) in place of \(C\) in the formula

Answer 15

so
\[\frac{ (J+3)(J) }{ ?}\]

Answer 16

like this?

Answer 17

You're on the right track. Finish it. Make sure you set it equal to \(t\) for consistency.

Answer 18

e.e hold on i just got lost

Answer 19

how am i finishing this?

Answer 20

How did you get lost. You were replacing \(C\) with the expression in the formula

Answer 21

yes ok so C= J+3 now what this is where i got lost

Answer 22

You did the numerator correctly. All you have to do it do the denominator.

Answer 23

\[\frac{ (J+3)(J) }{ (J+3)+(J)}\]

Answer 24

like this??

Answer 25

Exactly but set that equal to \(t\)

Answer 26

\[t=\frac{ (J+3)(J) }{ (J+3)+(J)}\]

Answer 27

Precisely

Answer 28

so now what

Answer 29

Now insert the given value for \(t\)

Answer 30

Do you know what it is? Do you remember what \(t\) represents? Go back to the previous question if you don't remember.

Answer 31

t represents time it takes to finish there objective

Answer 32

Is that amount given in the problem?

Answer 33

ummmmmmmm idk let me check the problem

Answer 34

tbh idk and i dont think it is

Answer 35

Go to the previous problem and find out what \(t\) represents

Answer 36

i just said t represents the time it takes to finish there objective as in painting

Answer 37

And what is the equivalent of that here? What's another word for "finish" in the problem?

Answer 38

complete e.e

Answer 39

Bingo. So do you have it now? What is the value of \(t\)?

Answer 40

ummmmmm not really so the value of t is c?

Answer 41

Read the problem to yourself once more. I'm not going to give this to you since it is so obvious.

Answer 42

oh wait so t=2

Answer 43

Correct

Answer 44

ok but what does that have to do with the time it takes Jennifer to do it her own

Answer 45

We will solve for \(J\). If you notice, the equation is all in terms of \(J\) now.

Answer 46

\[2=\frac{ (J+3)(J) }{ (J+3)+(J) }\]

Answer 47

So it looks like this????

Answer 48

Yes, but the next step is to add the J's in the denominator.

Answer 49

ok......

Answer 50

would it be 2J+3????

Answer 51

Correct

Answer 52

so it would look like
\[2=\frac{ (J+3)(J) }{ 2J+3 }\]

Answer 53

@Hero what next

Answer 54

Multiply both sides by the denominator

Answer 55

ok so after doing that would it equal 2J+3 = J(J+3)

Answer 56

Distribute \(J(J + 3)\)

Answer 57

it would equal

\[J^2+3J\]

Answer 58

i think atleast

Answer 59

Yes that is correct but remember, for consistency include what is on the other side of the equal sign.

Answer 60

Because the next step is to subtract \(2J\) from both sides

Answer 61

wait so
\[2=\frac{ (J+3)(J) }{ J^2+3J }\]
this is what it is

Answer 62

now we subtract 2j from both sides?

Answer 63

You're going backwards. You already multiplied both sides by the denominator? Remember?

Answer 64

Do you not remember being at this step: \(2J+3 = J(J+3)\)

We're not dealing with a fraction anymore

Answer 65

The next step was to distribute the expression on the RHS

Answer 66

ohhhhhhhhhh ok thats where i got lost i thought we where still doing that

Answer 67

Do you know where we are now?

Answer 68

If so, please post it

Answer 69

all i can think of is it would equal 4J+6 but i think i could be wrong

Answer 70

We were here:
\(2J+3 = J(J+3)\)

The next step was to distribute \(J(J + 3)\)

Answer 71

It's not a good idea to watch Hanna Montana at the same time you're doing math btw

Answer 72

e.e what

Answer 73

Nevermind

Answer 74

I'm just saying it is best not to be distracted while doing this

Answer 75

anyway i already did distribute it e.e

Answer 76

i got \[J^2+3J\]

Answer 77

Okay if you did, you should post that step here. Post the ENTIRE equation not just one side of it.

Answer 78

Look at my previous step if you need help.

Answer 79

wait what your previous step wait hold on either your going to fast or im getting lost again let me read for a second

Answer 80

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Hero
We were here:
\(2J+3 = J(J+3)\)

The next step was to distribute \(J(J + 3)\)
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 81

I ALREADY DISTRIBUTED IT LIKE 3 TIMES e.e

Answer 82

Yes, but show both sides of the equation

Answer 83

Both sides of the equation?

Answer 84

Showing both sides is confirmation you know what's going on

Answer 85

YES

Answer 86

ok hold on

Answer 87

i officially got nothing i have no idea what to do

Answer 88

We began with this
\[t=\frac{ CJ }{ C+J }\]

Then you figured out the expression for \(C\):
\[t=\frac{ (J+3)(J) }{ (J+3)+(J)}\]

Next you figured out the value of \(t\):
\[2=\frac{ (J+3)(J) }{ 2J+3 }\]

Then you multiplied both sides by the denominator to get:
\(2(2J + 3) = J(J + 3)\)

Answer 89

Notice the whole time we're dealing with expressions on both sides of the equal sign.

Answer 90

yes

Answer 91

Do you want me to also hightlight them in colors? At each step, you perform a step while showing both sides of the equal time.

Answer 92

equal sign*

Answer 93

I don't know how you got confused when we were going step by step. You seemed to be following.

Answer 94

i am following the best i can but its not easy for me to understand this

Answer 95

We began with this
\[t=\frac{ CJ }{ C+J }\]

Then you figured out the expression for \(C\):
\[t=\frac{ (J+3)(J) }{ (J+3)+(J)}\]

Next you figured out the value of \(t\):
\[2=\frac{ (J+3)(J) }{ 2J+3 }\]

Then you multiplied both sides by the denominator to get:
\(2(2J + 3) = J(J + 3)\)

Then we distributed and it equaled
\[J^2+ 3J\]

Answer 96

this is where i am

Answer 97

Right, so all you had to do is post the other side of the equation:
\(2(2J + 3) = J^2 + 3J\) I don't think it was difficult for you to realize what I was asking you to do. Post both sides of the equal sign at every step.

Answer 98

thats not what i thought you ment at all tbh sorry i thought you ment something different

Answer 99

Now you have to distribute the expression other side of the equation: \(2(2J + 3)\)

Answer 100

We began with this
\[t=\frac{ CJ }{ C+J }\]

Then you figured out the expression for \(C\):
\[t=\frac{ (J+3)(J) }{ (J+3)+(J)}\]

Next you figured out the value of \(t\):
\[2=\frac{ (J+3)(J) }{ 2J+3 }\]

Then you multiplied both sides by the denominator to get:
\(2(2J + 3) = J(J + 3)\)

Then we distributed and it equaled
\[J^2+3J\]
Now we have
\[2(2J+3)=J^2+3J\]
we must distribute again but this time on the other side
\[2(2J+3)=4J+6\]

Answer 101

like this?

Answer 102

Except you've now eliminated the other side of the equation that contains the \(J^2\)

Answer 103

\(4J + 6\) is correct though but that is only one side of the equation

Answer 104

You must include the other side of the original equation in the next step

Answer 105

It should be
\(4J + 6 = J^2 + 3J\)

Answer 106

I've never seen anyone get confused on this particular thing before.

Answer 107

Im sorry Hero i know im hard to work with ive been told that my whole life im horrible with math it just never soaks in

Answer 108

anyway now lets move on

Answer 109

so we now have the equation as

\(4J + 6 = J^2 + 3J\)

Answer 110

Yes, the next step is to subtract \(4J\) from both sides

Answer 111

ok and that would equal
\[J^2-J-6=0\]
then we must solve using the quadratic formula which would give us the finishing numbers of
J=3, J=-2?

Answer 112

Looks good to me

Answer 113

But of course you dis-regard the negative number

Answer 114

As there is no such thing as negative hours

Answer 115

so would the answer be Jennifer takes 3/2 hours to pain the room by her self

Answer 116

smh

Answer 117

There's only one answer

Answer 118

ik i just realized what i did hold on

Answer 119

Or rather, there is only one value of J

Answer 120

You have one positive value and one negative value. The negative value is dis-regarded because it makes no sense in terms of what the value of J represents.

Answer 121

so do we put it as 3,2 or 3/2 or 2/3 as our answer

Answer 122

@AnimeGhoul8863 there are two values of J. One of them we discard because the value is negative

Answer 123

I don't know how many times I have to say it before you "realize"

Answer 124

T~T i dont purposely not understand it geez sorry so the answer is 3 got it thanks for your help

Answer 125

Yes J = 3

Answer 126

thank you for the help i think i understand it more than i did to begin with

Answer 127

Glad to hear it.