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

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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

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.

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.

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

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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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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)

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

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

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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

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

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11 Nov 2017, 00:55

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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

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