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 ho

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Question 1165433: 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?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
           TIME Alone, hours             RATE in job per hour
Homer        x                           1/x
Mike        x-1                          1/(x-1)
Together                                 1/x+1/(x-1)

Following the description, 7%281%2Fx%2B1%2F%28x-1%29%29%2B6%281%2F%28x-1%29%29=1

Simplify and solve.


The work omitted here but Homer's time if working alone, x, appears to be about 20.66 hours or 20 hours 40 minutes.