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Work rate problem - 2

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Work rate problem - 2

by pratyoosh » Sun Nov 28, 2010 1:59 pm
Q. 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?
A. 1/3x
B. 3x/(x - 3)
C. (x - 3) / 3x
D. x / (x - 3)
E. (x - 3) / x

A: C
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by Rahul@gurome » Sun Nov 28, 2010 7:12 pm
Lindsay can paint 1/x part of a certain room in 20 minutes.
So in 1 hour = 60 minutes, he can paint 3/x part of a certain room.
Since Lindsay and Joseph combined can paint the whole room in 1 hour, part of room painted by Joseph in 1 hour is 1 - 3/x = (x-3)/x.
So part of room painted by Joseph in 20 minutes or 1/3 of an hour is (x - 3)/3x.

The correct answer is C.
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by pratyoosh » Sun Nov 28, 2010 11:56 pm
Brilliant, thanks Rahul.
Rahul@gurome wrote:Lindsay can paint 1/x part of a certain room in 20 minutes.
So in 1 hour = 60 minutes, he can paint 3/x part of a certain room.
Since Lindsay and Joseph combined can paint the whole room in 1 hour, part of room painted by Joseph in 1 hour is 1 - 3/x = (x-3)/x.
So part of room painted by Joseph in 20 minutes or 1/3 of an hour is (x - 3)/3x.

The correct answer is C.
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by Brent@GMATPrepNow » Tue Nov 05, 2019 6:13 am
pratyoosh wrote:Q. 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?
A. 1/3x
B. 3x/(x - 3)
C. (x - 3) / 3x
D. x / (x - 3)
E. (x - 3) / x

A: C
Given: Lindsay can paint 1/x of a certain room in 20 minutes
So, in 1 HOUR, Lindsay can paint 3/x of the room

Given: Lindsay and Joseph can paint the room in 1 HOUR.
During that one hour, Lindsay can paint 3/x of the room.
So, during that 1 HOUR, Joseph must paint the rest (whatever Lindsay did not paint)
So, during the 1 HOUR, the fraction of the room that Joseph paints = 1 - 3/x
= x/x - 3/x
= (x-3)/x

So, (x-3)/x = the fraction of the room that Joseph paints in one hour.
Since 20 minutes = 1/3 of an hour, Joseph can paint (1/3)[(x-3)/x] of the room in 20 minutes.
(1/3)[(x-3)/3x] = (x-3)/3x

Answer: C

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Answer

by [email protected] » Tue Nov 05, 2019 11:01 am
Hi All,

We're told that Lindsay can paint 1/X of a certain room in 20 minutes - and that Lindsay AND Joseph can paint the FULL room in 1 hour. We're asked what fraction of the same room can Joseph paint in 20 minutes on his own. This question can be solved in a couple of different ways, including by TESTing VALUES.

To start, the math involved would be really easy if BOTH Lindsay and Joseph paint at the same rate. Thankfully, we CAN choose values that will make that happen. If the two work at the same rate, then each will paint 1/2 the room in 1 hour. By extension, in 20 minutes (re: 1/3 of an hour), each would paint (1/3)(1/2) = 1/6 of the room every 20 minutes. Thus, let's TEST X = 6.... meaning that Lindsay paints 1/6 of the room in 20 minutes and Joseph also paints 1/6 of the room in 20 minutes.

We're looking for an answer that equals 1/6 when X = 6. There's only one answer that matches...

Final Answer: C

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