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# Will and Christine will work together to proofread a 420-page manuscri

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Math Expert
Joined: 02 Sep 2009
Posts: 50060
Will and Christine will work together to proofread a 420-page manuscri  [#permalink]

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11 Mar 2018, 21:06
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

71% (02:18) correct 29% (03:03) wrong based on 105 sessions

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Will and Christine will work together to proofread a 420-page manuscript. Will takes 4 minutes to proofread one page and Christine takes 3 minutes to proofread one page. If each proofreader, at maximum, can proofread for 18 hours, what is the fewest number of hours that Will will have to spend proofreading this manuscript?

A. 0 hours
B. 2 hours
C. 4 hours
D. 8 hours
E. 18 hours

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Joined: 07 Jan 2016
Posts: 781
Location: India
GMAT 1: 710 Q49 V36
Re: Will and Christine will work together to proofread a 420-page manuscri  [#permalink]

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12 Mar 2018, 00:14
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Bunuel wrote:
Will and Christine will work together to proofread a 420-page manuscript. Will takes 4 minutes to proofread one page and Christine takes 3 minutes to proofread one page. If each proofreader, at maximum, can proofread for 18 hours, what is the fewest number of hours that Will will have to spend proofreading this manuscript?

A. 0 hours
B. 2 hours
C. 4 hours
D. 8 hours
E. 18 hours

will 4 minutes to proof read - in one hour 15 pages ( 60min/4) and similarly christine takes 3 mins so in one hour 20 pages

18 hrs max = 20x18 = 360
rem = 420-360=60

will = 60/15 = 4
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Posts: 2576
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Re: Will and Christine will work together to proofread a 420-page manuscri  [#permalink]

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12 Mar 2018, 06:45
1
1
Bunuel wrote:
Will and Christine will work together to proofread a 420-page manuscript. Will takes 4 minutes to proofread one page and Christine takes 3 minutes to proofread one page. If each proofreader, at maximum, can proofread for 18 hours, what is the fewest number of hours that Will will have to spendproofreading this manuscript?

A. 0 hours
B. 2 hours
C. 4 hours
D. 8 hours
E. 18 hours

For Will to spend the fewest hours in proofreading, Christine must spend the maximum time(i.e.18 hours) proofreading the menuscript

Christine reads 1 page in 3 minutes

i.e. Christine reads 20 pages in 60 minutes (1 hours)

i.e. Christine reads 18*20=360 pages in 18 hours

Remaining pages = 420 - 360 = 60

Will time to proofread 60 pages = 60*4 = 240 min = 240/60= 4 hours

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Will and Christine will work together to proofread a 420-page manuscri  [#permalink]

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12 Mar 2018, 10:09
1
Bunuel wrote:
Will and Christine will work together to proofread a 420-page manuscript. Will takes 4 minutes to proofread one page and Christine takes 3 minutes to proofread one page. If each proofreader, at maximum, can proofread for 18 hours, what is the fewest number of hours that Will will have to spend proofreading this manuscript?

A. 0 hours
B. 2 hours
C. 4 hours
D. 8 hours
E. 18 hours

To minimize Will's time, maximize Christine's time, and thus, amount of work she completes.

Convert rates in minutes to rates in hours. For Christine, multiply 3 minutes by 20 to get 60 minutes = 1 hour. Multiply numerator by 20, too.

C's rate: $$(\frac{1p}{3min}*\frac{20}{20})=\frac{20p}{60mins}=\frac{20p}{1hr}$$

C completes how many pages?
$$W=R*T$$. Maximum T= 18 hrs
$$W$$ completed: (20 p/hr * 18 hrs) = 360 pages

Work remaining for Will: (420-360)= 60 pages

Will's rate: $$(\frac{1p}{4min}=\frac{15p}{60min})=\frac{15p}{1hr}$$

Will's time? 60 pages remain.$$T=\frac{W}{R}$$
Will needs only $$T =\frac{60p}{(\frac{15p}{1hr})}= 4$$ hours to finish

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Joined: 14 Aug 2017
Posts: 42
Concentration: Operations, Social Entrepreneurship
GMAT 1: 610 Q48 V26
Re: Will and Christine will work together to proofread a 420-page manuscri  [#permalink]

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16 Mar 2018, 11:11
Will will be reading 15 pages an hour --- Christine will be reading 20 pages an hour.

15x+20y=420
For x to be minimum, make Y maximum
x=28-4/3Y

X=4 Hours.
Re: Will and Christine will work together to proofread a 420-page manuscri &nbs [#permalink] 16 Mar 2018, 11:11
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