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

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

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New post 10 Aug 2006, 09:03
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Laura 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?

A. 1/(3x)
B. 3x/(x-3)
C. (x – 3)/(3x)
D. x/(x-3)
E. (x-3)/x
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Apr 2014, 23:11, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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New post 10 Aug 2006, 09:16
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Given
rLaura = 1/x room in 20 minute

rL = 1/(x/3) room/hr

Let rJ = 1/j be Joseph's rate

1/(x/3) + 1/j = 1

or 3/x + 1/j = 1
or 3j+x = xj

or x/(x-3) = j

Therfore, rJ = 1/(x-3)/x room/hr

60 minutes : (x-3)/x room
20 : (x-3)/3x

Answer : C : (x-3)/3x

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New post 10 Aug 2006, 09:16
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20 minutes is 1/3 of an hour. In an hour, Laura would paint
3 * 1/x = 3/x;
Joseph, then, would have painted the rest:
1 - 3/x, or (x-3)/x.
So in 20 minutes Joe would do
(x-3)/3x.

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New post 10 Aug 2006, 09:45
Good one haas and brain... i was stuck on how to start this one out but you guys are right on the nose..


C.

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New post 10 Aug 2006, 09:48
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braindancer's solution is much more elegant and intuitive... like that!!

Thanks brain/.

braindancer wrote:
20 minutes is 1/3 of an hour. In an hour, Laura would paint
3 * 1/x = 3/x;
Joseph, then, would have painted the rest:
1 - 3/x, or (x-3)/x.
So in 20 minutes Joe would do
(x-3)/3x.

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New post 10 Aug 2006, 10:01
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3(1/x) +3(1/y) = 1

(1/y) = 1/3 - 1/x

1/y = (x-3)/3x

3-C

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New post 10 Aug 2006, 10:51
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I did it in a simpler way

Laura's 1 hour work = 3/x
Joseph's one hour work = y

Laura' sand Joseph's 1 hour work = 1 ( as given they completed full work in one hour).

So 3/x + y = 1
i.e y = (x-3)/x

So Joseph's 20 minutes work = (x-3)/3x
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New post 11 Aug 2006, 01:02
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Laura can paint 1/x of room in 20 mins
Hence in 1 min she can paint 1/20x of room

Let Joseph paints 1/J of the room in 1 min

Hence
1/20x + 1/J = 1/60
1/J = x-3/60x
Hence J= 60x/x-3

Therefore in 60x/x-3 mins joseph paints 1 room
in 20 mins he can paint = 20 * (x-3) / 60x = (x-3)/3x of the room

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Re: Laura can paint 1/x of a certain room in 20 minutes. What [#permalink]

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Rate of Laura \(= \frac{1}{20x}\) (Per Min)

Consider rate of Joseph \(= \frac{1}{j}\) (Per Min)

Both combined perform the task in 60 minutes

\(\frac{1}{20x} + \frac{1}{j} = \frac{1}{60}\)

\(\frac{1}{j} = \frac{1}{60} - \frac{1}{20x}\)

\(\frac{1}{j} = \frac{x-3}{60x}\) (Per Min)

So in 20 minutes, work done by Joseph

\(= \frac{x-3}{60x} * 20\)

\(= \frac{x-3}{3x}\)

Answer = C
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Re: Laura can paint 1/x of a certain room in 20 minutes. What [#permalink]

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New post 24 Apr 2014, 21:09
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rkatl wrote:
Laura 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?

A. 1/(3x)
B. 3x/(x-3)
C. (x – 3)/(3x)
D. x/(x-3)
E. (x-3)/x



The Question is a good candidate for plugin...Here is how I would approach

Let us assume value of x for laura to be 12 so we have that laura does 1/12th of room in 20 minutes or to paint one complete laura takes 240 minutes

Let Joseph take y minutes to paint 1 room so we have
Also given that
1/240 +1/y = 1/60 ----> Solve for y and we get y =240/3 or 80 minutes.
(Here we should choose the value of x in such a way that 1/y = \((1/60- 1/x)\geq{0}\) so that y is not negative.


So Joseph paints 1 room in 80 minutes so in 20 minutes, he will paint 1/4th of the room.

Plug in value of x in the above options and we get answer C.
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Re: Laura can paint 1/x of a certain room in 20 minutes. What [#permalink]

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New post 22 Sep 2015, 05:32
rkatl wrote:
Laura 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?

A. 1/(3x)
B. 3x/(x-3)
C. (x – 3)/(3x)
D. x/(x-3)
E. (x-3)/x



This is a very easy question...

it is given in the question that L completes the (1/x)th of a work in 20 minutes. So she completes 3/xth of a work in 60 minutes.

the job is finished by both of them in 1 hour.. so in 60 minutes the other fraction of work i.e (1- (3/x)) is done by Joseph.

So Joseph does (x-3)/x of a work in 60 minutes. So in 20 minutes he would have done only (1/3)rd of it = (1/3)((x-3)/x)

which is (x-3/3x)--> Choice C

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Re: Laura can paint 1/x of a certain room in 20 minutes. What [#permalink]

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New post 23 Sep 2015, 08:58
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rkatl wrote:
Laura 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?

A. 1/(3x)
B. 3x/(x-3)
C. (x – 3)/(3x)
D. x/(x-3)
E. (x-3)/x


Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete 120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6

Answer (C)
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Laura can paint 1/x of a certain room in 20 minutes. What [#permalink]

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New post 14 Nov 2015, 12:39
J's rate=1-3/x
J's time=1/3 hour
(1-3/x)(1/3)=x-3/3x

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Re: Laura can paint 1/x of a certain room in 20 minutes. What [#permalink]

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New post 18 Sep 2016, 08:31
rkatl wrote:
Laura 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?

A. 1/(3x)
B. 3x/(x-3)
C. (x – 3)/(3x)
D. x/(x-3)
E. (x-3)/x


Together they paint 1 room in 60 min. So in 20 min they paint (1/3) room. Out of this Laura painted (1/x) room, so Joseph must have painted (1/3) - (1/x) room => (x – 3)/(3x) room

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Re: Laura can paint 1/x of a certain room in 20 minutes. What [#permalink]

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

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New post 11 Nov 2017, 22:55
rkatl wrote:
Laura 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?

A. 1/(3x)
B. 3x/(x-3)
C. (x – 3)/(3x)
D. x/(x-3)
E. (x-3)/x

Convert everything in terms of 20 min.

Let the part of the room painted by Joseph in 20 min be 1/y

In 20 min, we have part of work done as 1/x +1/y=20/60=1/3

1/y=1/3 - 1/x = (x-3)/(3x)
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