Question

It takes Julia 12 hours to tar a roof, Shayna can tar the same room in 15 hours. Find how long it would take them if they did it together.
So far i got
1/x= 1/12+1/15
1/x=15/180+12/180
is this right so far?

Answer 1

@hero :) :) :) :) :)

Answer 2

It looks right, but there's a much easier way to solve it.

Answer 3

Uhh how?

Answer 4

It is a pretty simple expression called the "working together expression". If two people, J and S, can each complete a task alone, then together they can complete the task in \(\large\frac{J \times S}{J + S}\) amount of time.

Answer 5

so.. just multiply js on the num and add them on the dem?

Answer 6

Try it out and see what happens, but make sure you post your result so that I know you are doing it correctly.

Answer 7

I got 180/27.

Answer 8

Are you going to divide that to get a more meaningful result?

Answer 9

6.66?

Answer 10

like repeating

Answer 11

6.67 or 6 and 2/3 hours.

Answer 12

to be exact. Either way, doing it that way is much quicker.

Answer 13

Okay since its asking to round to the nearest hundredth then i could do 6.67? and also How would i do it if it asked for them to be working alone instead of together?

Answer 14

Of course, you might want to learn some simplification methods for the fractions.

Answer 15

think of a clock. what is 2/3 of an hour ?

Answer 16

Alright and I could do this method for any of the time based problems?

Answer 17

If it asks, for example, how much did J do alone, then you input everything given into the expression

\[\frac{J \times S}{J + S} = t\], then solve for J.

Answer 18

Suppose you didn't know J, but only knew how much S can do alone, and how much J and S can do together, then you would have:

\[\frac{J \times 15}{J + 15} = 6\frac{2}{3}\]

Then all you would have to do is simply solve for J by doing some simple mathematical manipulation.

Answer 19

I'm lost. Okay like my next question is like working together mark and wilbur can clean the attic in 6.3 hours. Had he done it alone it would have taken him 17 hours. How long would it take mark to do it alone. Would i then do
6.3/17?

Answer 20

By he, they meant Wilbur. and we have to find M

Answer 21

But anyway to solve:

You define your variables as:

M = the work Mark can do alone
W = the work Wilbur can do alone
t = the time they can do the work together

You define your working together equation as follows:
\[\frac{M \times W}{M + W} = t\]

You define your working together equation as follows:
\[\frac{M \times 17}{M + 17} = 6.3\]

Answer 22

So now, all you have to do is just solve for M. Sorry for the confusion.

Answer 23

By the way, figuring out what to do is just a matter of using the working together equation. All you do is just plug in the appropriate values and solve. But make sure you have the variables properly defined.

Answer 24

So far i have m17 /m+17= 6.3. So would i add the 17 to the m? or just cross them out

Answer 25

No, you can't cross anything out. You have to simply figure out how to isolate M. You might want to begin by figuring out how to get rid of the denominator on the left side. By 'get rid of' I don't mean cross anything out. I mean perform the mathematical manipulation necessary to work towards isolating M.

Answer 26

multiply the 17 by both sides

Answer 27

No, no. You have to treat the (M + 17) in the denominator as one expression or one number.

Answer 28

So then it would be two separate problems. mx17= 6.3 and m+17 = 6.3

Answer 29

hm.

Answer 30

No it will not. This isn't the zero product property.

Answer 31

Okay well other than that , I'm completely lost. You can't add the M to the 17. And there both the same so.....it would just cancel out. Other than that guess i don't know the next step

Answer 32

\[\frac{ M * 17 }{ M + 17 } = 6.3 \rightarrow M * 17 = 6.3(M + 17)\]

Answer 33

explain...

Answer 34

just multiply both sides by (M + 17), that will cancel it on the left side

Answer 35

couldn't you have done that with the addition side too?

Answer 36

What exactly do you mean by the "addition" side?

Answer 37

not sure what you mean?

in general if

\[\frac{ a }{ b } = c\]

then

\[a = bc\]

assuming b is not 0

Answer 38

There's only two sides to an equation. A right side and a left side. There's no "addition" side.

Answer 39

okay but how did it go from a fraction to an equation.

Answer 40

it always was an equation, right? it started as an equation with a fraction on the left hand side, and a single number on the right hand side

Answer 41

@Artchicky, if you had to solve

\[\frac{2x + 4}{5} = 9\]

What would you do first?

Answer 42

I would do the 5 first.

Answer 43

What would you do with the 5?

Answer 44

times it by the 2x+4 and the 9

Answer 45

Okay, and why would you do that? For what purpose?

Answer 46

to get rid of the fraction

Answer 47

Okay, so basically, whatever is in the denominator of the fraction, you multiply both sides of the equation by that to get rid of the fraction. So, for the equation we are currently working on, why would we do anything different?

Answer 48

In order to get rid of the fraction, we multiply both sides of the equation by the whole expression in the denominator, not just part of it, but the whole thing. So not just 17, but M + 17.

Answer 49

oh because thats whats on the bottom. I get it

Answer 50

ya, then continue solving from there.

Answer 51

17m= 6.3m+ 107.1?

Answer 52

Okay, continue solving for m. You have to place like terms on the same side, right? I'm pretty sure you know how to do that.

Answer 53

10.0

Answer 54

You mean M = 10. That is correct.

Answer 55

This wasn't as difficult as you made it out to be.

Answer 56

well it went from an equation to a problem with two people putting out two different problems.

Answer 57

There's more than one way to solve math problems. That's the general consensus. I was trying to show you a method that was supposed to be an easier, simpler method. However, for some reason, you seemed to have trouble solving the fractional equation, with the most confusing thing for you being how to properly isolate the variable M. But hopefully you have it now.

Answer 58

Yes i understand it

Answer 59

The method I was showing you was a three step process:

1. Get rid of the denominator
2. Distribute
3. Isolate the variable

The method saifoo.khan showed you involves finding LCDs and such, which is fine, but it is always good to have an alternative method.

Answer 60

The working together expression works best when you know how much time both of a job persons can finish alone and need to find how much time it takes if they work together.