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

Algebra ->  Rate-of-work-word-problems -> 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       Log On


   

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) About Me  (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.
%281%2Fh%29+%2B+%281%2Fd%29+%2B+%281%2Fl%29+=+1%2F4
%281%2Fh%29+%2B+%281%2Fl%29+=+1%2F6
%281%2Fd%29+%2B+%281%2Fl%29+=+1%2F7
add the bottom two equations to get
%281%2Fh%29+%2B+%282%2Fl%29+%2B+%281%2Fd%29+=+%2813%2F42%29
%281%2Fh%29+%2B+%281%2Fl%29+%2B+%281%2Fd%29+=+%2813%2F42%29+-+%281%2Fl%29
Recall the first equation and make a substitution.
%281%2F4%29+=+%2813%2F42%29+-+%281%2Fl%29
%2813%2F42%29-%281%2F4%29+=+%281%2Fl%29
%2826%2F84%29-%2821%2F84%29+=+%285%2F84%29+=+%281%2Fl%29
5l+=+84
l+=+84%2F5} or 16.8 hours or 16 4/5 hours
Plug l = 84/5 into the 2nd equation to get
1%2Fh+%2B+5%2F84+=+1%2F6
1%2Fh+=+5%2F84+=+14%2F84
1%2Fh+=+9%2F84
h+=+84%2F9 or 9.33333 hours or 9 1/3 hours
Plug l = 84/5 into the 3rd equation to get
1%2Fd+%2B+5%2F84+=+1%2F7
1%2Fd+=+7%2F84
d+=+84%2F7 or 12 hours.