SOLUTION: Painter Painter has three employees: Huey, Dewey, and Louie. Working together they can paint a large room in 4 hours. Huey and Louie can paint the same size room in 6 hours. Dewey

Question 445162: Painter Painter has three employees: Huey, Dewey, and Louie. Working together they can paint a large room in 4 hours. Huey and Louie can paint the same size room in 6 hours. Dewey and Louie can paint the same size room in 7 hours. How long would it take each of them to paint the room alone?
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Let h,d, and l be the number of hours it takes for each to separately paint a room.
So here's the trick: the efficiency of each is (1 room) / (number of hours it takes). In essence, it's the fraction of the room painted in 1 hour.

add the bottom two equations to get

Recall the first equation and make a substitution.

} or 16.8 hours or 16 4/5 hours
Plug l = 84/5 into the 2nd equation to get

or 9.33333 hours or 9 1/3 hours
Plug l = 84/5 into the 3rd equation to get

or 12 hours.

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