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Jonathan can type a 20 page document in 40 minutes, Susan

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timmaxwell8
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Jonathan can type a 20 page document in 40 minutes, Susan [#permalink] New post   Updated on: 09 Feb 2012, 13:58
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Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?

A. 5 minutes
B. 10 minutes
C. 15 minutes
D. 18 minutes
E. 20 minutes
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B

Originally posted by timmaxwell8 on 12 Oct 2009, 12:42.
Last edited by Bunuel on 09 Feb 2012, 13:58, edited 1 time in total.
Edited the question and added the OA
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gmatjon
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Re: Working together question [#permalink] New post   12 Oct 2009, 21:13
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You may set up common equation like this:

job/A+job/B+job/C=job/x
Memorize this universal formula, you will need it definitely for GMAT.

and find x from this equation
In this specific case, the equation will look like this:

20/40+20/30+20/24=20/x
If you solve this equation, you get the same answer D (10)

If you like my post, please give me kudos. :)
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Bunuel
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Re: Working together question [#permalink] New post   12 Oct 2009, 13:00
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timmaxwell8 wrote:
30. Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?

A. 5 minutes
B. 10 minutes
C. 15 minutes
D. 18 minutes
E. 20 minutes


J=20/40=1/2per min
S=20/30=2/3per min
JK=20/24=5/6per min

In one min together 1/2+2/3+5/6=12/6=2 pages.

For 20 pages=20/2=10

B.
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Re: Working together question [#permalink] New post   13 Oct 2009, 10:23
I will go with option B)10
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Re: Working together question [#permalink] New post   13 Oct 2009, 10:54
Bunuel wrote:
timmaxwell8 wrote:
30. Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?

A. 5 minutes
B. 10 minutes
C. 15 minutes
D. 18 minutes
E. 20 minutes


J=20/40=1/2per min
S=20/30=2/3per min
JK=20/24=5/6per min

In one min together 1/2+2/3+5/6=12/6=2 pages.

For 20 pages=20/2=10

B.



If the work involved here is to type the 20page document we can even avoid calculating time taken per page.
will this apporach backfire?

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Asterix
"Time is of gr8 essence"
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Re: Working together question [#permalink] New post   13 Oct 2009, 11:14
1/40+1/30+1/24 = 24/240 = 1/10 work per min = 10 min to complete work :wink:
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Re: Working together question [#permalink] New post   17 Oct 2009, 23:32
Formula for time taken by 3 guys is:

t1*t2*t3 / ( t1*t2 + t2*t3 + t3*t1 ) , this might be lead to a faster calculation :)
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Re: Jonathan can type a 20 page document in 40 minutes, Susan [#permalink] New post   28 Nov 2017, 08:51
Apply W=R*T formula

r(Johnathan)=1/2
r(Susan)=2/3
r(Jack)=5/6

1/2+2/3+5/6
r(total)=2 pages/minute

Therefore , applying this back to rate work formula, we get

20=2*T
T=10 minutes

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Re: Jonathan can type a 20 page document in 40 minutes, Susan [#permalink] New post   29 Nov 2017, 18:11
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timmaxwell8 wrote:
Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?

A. 5 minutes
B. 10 minutes
C. 15 minutes
D. 18 minutes
E. 20 minutes


Jonathan has a rate of 20/40 = 1/2 page per minute, Susan has a rate of 20/30 = 2/3, and Jack has a rate of 20/24 = 5/6.

The combined rate of all 3 is:

1/2 + 2/3 + 5/6 = 3/6 + 4/6 + 5/6 = 12/6 = 2. Thus, if we let t = the time it takes them to work together:

2t = 20

t = 10

Answer: B
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Re: Jonathan can type a 20 page document in 40 minutes, Susan [#permalink] New post   30 Nov 2017, 20:03
In 1 minute:
- Jonathan can type: 20/40 = 1/2 page
- Susan can type: 20/30 = 2/3 page
- Jack can type: 20/24 = 5/6 page
=> if they work together, in 1 minute they can type: 1/2 + 2/3 + 5/6 = 2 pages
=> It takes 20/2 = 10 minutes to type a 20 page document.
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Re: Jonathan can type a 20 page document in 40 minutes, Susan [#permalink] New post   06 Nov 2021, 02:08
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Re: Jonathan can type a 20 page document in 40 minutes, Susan [#permalink]
06 Nov 2021, 02:08
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