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I'm looking for a good formula/system to use for these problems. Too often I'm just relying on raw intuition and it takes me too much time to solve these questions. Is there a good starting place to solve these problems? What's like a good step 1 and step 2?

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

So I don't know a good way to start. I thought output = rate * time but what is it here? Let me think.... So rate * time = output. Okay. What else? Well, rates add onto each other without synergy... this is an assumption about rate problems on the GMAT. So if Machine A completes a 1/12 of a job in 1 hour and machine B completes 2/12 of a job in 1 hour, the two machines combined complete 3/12 of a job in 1 hour.

Is it 6 * r * 12 = 1 72r = 1 r = 1/72??

Why does that makes sense? Can I just arbitrarily make the job = 1?

So 1/72 is the rate of 1 machine.

x * 1/72 * 8 = 1 x = 9

So the answer is 9-6 = 3

What's a good way to think about this?

Someone, in a not very helpful way, suggested multiplying 6 * 12... but that doesn't explain to me what to do.

The answer is 3.

YuiTo Cheng
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Jwan622
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  • The rate is always the same, you can forget it.But you forgot about the main thing:The number of machines! Consider that the otput rate should stay constant, and you should be done :) – chubakueno Dec 16 '13 at 06:32
  • About the edit: The important thing here is that the job stays constant. It could equal $\pi$ , if you feel like so. – chubakueno Dec 16 '13 at 06:39
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    I machine will take $72$ days, so it takes $9$ machines to do the job in $8$ days. Or else we need $m$ machines, where $\frac{m}{6}=\frac{12}{8}$. – André Nicolas Dec 16 '13 at 06:42
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    @Jwan622: I see you have posted 22 questions and have accepted 0 answers. Take a look at this. – JohnD Dec 16 '13 at 16:07
  • ah I'm going through my list now. Thanks! Sorry I'm getting to know the etiqutte here. I'll learn quickly! – Jwan622 Dec 16 '13 at 16:28
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    @Jwan622: No problem, I understand and just wanted to help you in that regard since it might end up motivating more people to answer your questions. – JohnD Dec 16 '13 at 16:37

2 Answers2

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Think job = rate * time. Then $j=6r*12$ and $j=(6+x)r*8$ where $x$ is the number of machines to be added. Set these equal, divide out $r$, and solve for $x$ to get $x=3$.

JohnD
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Any time you have multiple machines working together, you add their rate to get the total rate. In this case, the machines all have the same rate, so their total rate for the 6 machines is just 6r. We know that rate*time=work, so we know that 6r*12days=W (W can represent the job they complete)

Now we want to know how many more machines need to be added to complete the job in 8 days. We can represent that like this xr*8days=W. I find it easier to start by just making it x then subtracting the 6 later to avoid additional needless computation. since, they are both completing the same job, we know that xr*8=6r*12 and solve for x x=9, once we subtract the original 6 we get our answer 3

Eliza
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