SOLUTION: Homer and Mike were replacing the boards on​ Mike's old deck. Mike can do the job alone in 1 hour less time than Homer. They worked together for 7 hours until Homer had to go hom

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Question 1134522: Homer and Mike were replacing the boards on​ Mike's old deck. Mike can do the job alone in 1 hour less time than Homer. They worked together for 7 hours until Homer had to go home. Mike finished the job working by himself in an additional 6 hours. How long would it have taken Homer to fix the deck​ himself?
Found 2 solutions by josgarithmetic, Shin123:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Homer's rate 1%2Fh
Mike's rate 1%2F%28h-1%29
-

7%281%2Fh%2B1%2F%28h-1%29%29%2B6%2F%28h-1%29=1
Solve for h.

Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Homer can work alone in x hours.
%287%2Fx%29%2B7%2F%28x-1%29=%2814x-7%29%2Fx%28x-1%29
%2820x-13%29%2Fx%28x-1%29=1
x%5E2-x=20x-13
x%5E2-21x%2B13=0
x=%2821%2Broot%282%2C389%29%29%2F2 which is about 20.362 hours.