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

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Bunuel
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Will and Christine will work together to proofread a 420-page manuscri [#permalink] New post   11 Mar 2018, 21:06
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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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C
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Re: Will and Christine will work together to proofread a 420-page manuscri [#permalink] New post   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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Re: Will and Christine will work together to proofread a 420-page manuscri [#permalink] New post   12 Mar 2018, 06:45
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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 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



ANswer: Option C
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Will and Christine will work together to proofread a 420-page manuscri [#permalink] New post   12 Mar 2018, 10:09
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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

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

Answer C
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Re: Will and Christine will work together to proofread a 420-page manuscri [#permalink] New post   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

Start with y=18
X=4 Hours.
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Re: Will and Christine will work together to proofread a 420-page manuscri [#permalink] New post   22 Aug 2022, 03:59
Christine reads 1 page in 3 minutes

Christine reads 20 pages in 60 minutes (1 hours)

Will reads 1 page in 4 minutes

Will reads 15 page in 60 minutes

To minimize the hours of Will, we have to maximize the hours of Christine

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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Re: Will and Christine will work together to proofread a 420-page manuscri [#permalink]
22 Aug 2022, 03:59
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