SOLUTION: The OfficeJet printer can copy Maria's dissertation in 14 min. The LaserJet printer can copy the same document in 8 min. If the two machines work together, how long would they take

Question 158867: The OfficeJet printer can copy Maria's dissertation in 14 min. The LaserJet printer can copy the same document in 8 min. If the two machines work together, how long would they take to copy the dissertation?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let t=time it takes both machines working together to copy the dissertation
Officejet copies at the rate of 1/14 dissertaion per min
Laserjet copies at the rate 1/8 dissertaion per min
Together they copy at the rate of:
1/14 + 1/8 =4/56 + 7/56=11/56 dissertation per min
So, our equation to solve is:
(11/56)t=1 (1 dissertation, that is) multiply each side by 56
11t=56 divide each side by 11
t=5.09 min----time it takes both machines working together
Another way to look at it:
Together, the machines copy at the rate of 1/t dissertation per min, so:
1/14 + 1/8 =1/t multiply each term by 56t
4t+7t=56
11t=56----same as before
CK
(1/14)*5.09+(1/8)*5.09=1 multiply each term by 56
4*5.09+7*5.09=56
20.36 + 35.63=56
55.99~~~~~~56 roundoff error

Hope this helps---ptaylor

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