SOLUTION: Mercy can prepare a manuscript in 6 hours. Eunice can prepare it in 4 hours. How Long would it take them to preapre the manuscript together?

Question 112133: Mercy can prepare a manuscript in 6 hours. Eunice can prepare it in 4 hours. How Long would it take them to preapre the manuscript together?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=time it takes Mercy and Eunice working together to prepare a manuscript
Mercy prepares manuscripts at the rate of 1/6 manuscript per hour
Eunice prepares manuscripts at the rate of 1/4 manuscript per hour
Together, they prepare manuscripts at the rate of (1/6)+(1/4)=4/24+(6/24) or
10/24=5/12 manuscripts per hour.
So the question boils down to the following:
If Mercy and Eunice can prepare 5/12 of a manuscript per hour, how long will it take them working together to prepare 1 manuscript? So our equation to solve is:
(5/12)x=1 multiply each term by 12
5x=12 divide both sides by 5
x=2.4 hours------------time it takes Mercy and Eunice working together to prepare a manuscript
CK
(5/12)*2.4=1
12/12=1
1=1

Hope this helps---ptaylor
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