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# Lindsay can paint 1/x of a certain room in 20 minutes. What

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Manager
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Lindsay can paint 1/x of a certain room in 20 minutes. What [#permalink]

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02 Feb 2008, 06:20
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Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?

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SVP
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Re: PS MGMAT: Work problem [#permalink]

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02 Feb 2008, 07:52
are we supposed to be able to come up with an absolute number for the final answer, or wil it be in terms of a variable ? or, am i just really missing something ?

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Manager
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Re: PS MGMAT: Work problem [#permalink]

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02 Feb 2008, 08:08
Lindsay: 20 mins - 1/x of job, so in 60 mins - 3/x of job
Let's say Joseph completes y of job in 1 hr

we have 3/x + y = 1; y = 1-3/x = x-3/x of job in 1 hr

in 20 mins (x-3)/3x

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Senior Manager
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Re: PS MGMAT: Work problem [#permalink]

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02 Feb 2008, 12:04
Rate at which Lindsay can paint is $$\frac{1}{20x}$$ per minute.

Let rate at which Joseph can paint be $$\frac{1}{20y}$$ per minute.

We need to find $$\frac{1}{y}$$ -- the amount of work Joseph can do in 20 minutes.

$$\frac{60}{20x} + \frac{60}{20y} = 1$$

=> $$\frac{3}{x} + \frac{3}{y} = 1$$

=> $$\frac{3}{y} = 1- \frac{3}{x}$$

=> $$y = \frac{3x}{x-3}$$

=> $$\frac{1}{y} = \frac{x-3}{3x}$$
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Re: PS MGMAT: Work problem [#permalink]

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02 Feb 2008, 12:22
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CaspAreaGuy wrote:
Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?

Lindsay can paint 1/x of a certain room in 20 minutes
Lindsey and Joseph can paint 1/3 of room in 20 minuets.
so Joseph can paint the room 1/3 - 1/x in 20 minuets
so the fraction = (x - 3)/3x
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Senior Manager
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Re: PS MGMAT: Work problem [#permalink]

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02 Feb 2008, 12:32
GMAT TIGER wrote:
CaspAreaGuy wrote:
Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?

Lindsay can paint 1/x of a certain room in 20 minutes
Lindsey and Joseph can paint 1/3 of room in 20 minuets.
so Joseph can paint the room 1/3 - 1/x in 20 minuets
so the fraction = (x - 3)/3x

+1 for the approach. Much faster and cleaner....good one gmat tiger.
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Re: PS MGMAT: Work problem   [#permalink] 02 Feb 2008, 12:32
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# Lindsay can paint 1/x of a certain room in 20 minutes. What

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