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

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Q47  V34 GMAT 2: 660  Q46  V35 GMAT 3: 700  Q49  V36
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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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Q48  V18
1/40+1/30+1/24 = 24/240 = 1/10 work per min = 10 min to complete work
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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]
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

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
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Re: Jonathan can type a 20 page document in 40 minutes, Susan [#permalink]
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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Jonathan can type a 20 page document in 40 minutes, Susan [#permalink]
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]
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Re: Jonathan can type a 20 page document in 40 minutes, Susan [#permalink]
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