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

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Intern
Joined: 08 Oct 2009
Posts: 7
Jonathan can type a 20 page document in 40 minutes, Susan  [#permalink]

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Updated on: 09 Feb 2012, 12:58
2
2
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:55) correct 21% (02:21) wrong based on 285 sessions

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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

Originally posted by timmaxwell8 on 12 Oct 2009, 11:42.
Last edited by Bunuel on 09 Feb 2012, 12:58, edited 1 time in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 64144

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12 Oct 2009, 12:00
1
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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12 Oct 2009, 20:13
4
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)

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Manager
Joined: 15 Sep 2009
Posts: 83

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13 Oct 2009, 09:23
I will go with option B)10
Manager
Joined: 12 Oct 2009
Posts: 91

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13 Oct 2009, 09:54
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?

Regards
Asterix
"Time is of gr8 essence"
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Joined: 18 Jul 2009
Posts: 123
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Schools: South Asian B-schools

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13 Oct 2009, 10:14
1/40+1/30+1/24 = 24/240 = 1/10 work per min = 10 min to complete work
Director
Joined: 01 Apr 2008
Posts: 561
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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17 Oct 2009, 22:32
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
Intern
Joined: 30 Sep 2017
Posts: 15
Re: Jonathan can type a 20 page document in 40 minutes, Susan  [#permalink]

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28 Nov 2017, 07:51
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]

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29 Nov 2017, 17:11
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

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Intern
Joined: 12 Oct 2017
Posts: 34
Re: Jonathan can type a 20 page document in 40 minutes, Susan  [#permalink]

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30 Nov 2017, 19:03
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] 30 Nov 2017, 19:03