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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