Work Rate Question

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MI3: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Sat Feb 26, 2011 11:22 amFollowed by: 1 member; Thanked: 1 times

by MI3 » Mon May 23, 2011 9:14 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

Ans - C[/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon May 23, 2011 9:14 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon May 23, 2011 9:48 pm

MI3 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

Ans - C[/spoiler]

Lindsay can paint 1/x of a certain room in 20 minutes implies (1/x) Ã· 20 = 1/20x
Let John can paint 1/F of the room in 20 minutes.
Then 1/20x + 1/20F = 1/60
1/x + 1/F = 1/3
1/F = 1/3 - 1/x = (x - 3)/3x

The correct answer is C.

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MI3: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Sat Feb 26, 2011 11:22 amFollowed by: 1 member; Thanked: 1 times

by MI3 » Mon May 23, 2011 9:55 pm

Hello Anurag,

Thank you for getting back to me, but would you also mind clarifying the following: 1/20x and 1/20F would be the "rate" of work for Lindsay and John respectively, so I don't get how you have formed the third equation of > 1/20x + 1/20F = 1/60.

W = R * T

So in this case, how is the rate getting equated to (presumably) the time?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon May 23, 2011 9:59 pm

MI3 wrote:Hello Anurag,

Thank you for getting back to me, but would you also mind clarifying the following: 1/20x and 1/20F would be the "rate" of work for Lindsay and John respectively, so I don't get how you have formed the third equation of > 1/20x + 1/20F = 1/60.

W = R * T

So in this case, how is the rate getting equated to (presumably) the time?

1/20x is the work done by Lindsay in 1 minute and 1/20F is the work done by John in 1 minute.
So, 1 minute work by Lindsay + John = 1/20x + 1/20F, which is equal to 1/60 (As 1 hr = 60 minutes)

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue May 24, 2011 2:58 am

MI3 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

Ans - C[/spoiler]

Let job = 30 units, let x=5.
In 20 minutes, Lindsay produces (1/x)*30= (1/5)*30 = 6 units.
Thus, in 60 minutes, Lindsay produces 3*6 = 18 units.
Since the job is completed in an hour, work produced by Joseph = 30-18 = 12 units.
Thus, in 20 minutes -- 1/3 the time -- Joseph completes (1/3)*12 = 4 units.
Fraction of the job completed by Joseph in 20 minutes = 4/30 = 2/15. This is our target.

Now we plug x=5 into the answers to see which yields our target of 2/15.

Only answer choice C works:
(x-3)/3x = (5-3)/(3*5) = 2/15.

The correct answer is C.

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MI3: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Sat Feb 26, 2011 11:22 amFollowed by: 1 member; Thanked: 1 times

by MI3 » Tue May 24, 2011 10:57 am

Understood. Thank you.

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djiddish98: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Fri Jan 14, 2011 10:01 am; Thanked: 10 times

by djiddish98 » Tue May 24, 2011 1:38 pm

Anurag@Gurome wrote: 1/F = 1/3 - 1/x = (x - 3)/3x

Dumb question - How did you get from 1/3 - 1/x to (x-3)/3x? I can see that the results are equal (x/3x = 1/3 and 3/3x = 1/x), but I can't arithmetically get there.

Edit: Nevermind I got it.

1/F = 1/3 - 1/x -> x/f = x/3-1 -> 3x/f = x-3 -> 1/f = (x-3)/3x.

The tricky part is that we need to solve for 1/F, not F. I kept getting the inverse as the answer before I realized that

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