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 3 hours until Homer had to go home.

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Question 889518: 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 3 hours until Homer had to go home. Mike finished the job working by himself in an additional 3 hours. How long would it have taken Homer to fix the deck himself?
It will take Homer appropriately ___ hours ____ minutes to fix the deck by himself.
(Round to the nearest minute as needed).
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates Situation for Doing A Job, RT=J rate time job
----
Individual Rates:
Homer, 1/x
Mike, 1/(x-1)
x=time for Homer alone to do the one job.


They worked together for 3 hours
%281%2Fx%29%2A3%2B%281%2F%28x-1%29%29%2A3, the amount of job done.

Mike finished the job working by himself in an additional 3 hours.
%281%2F%28x-1%29%29%2A3,Finishing the undone part of the job.

Both of those parts make a sum of 1 whole job.
highlight%28%281%2Fx%29%2A3%2B%281%2F%28x-1%29%29%2A3%2B%281%2F%28x-1%29%29%2A3=1%29;
Understanding how this equation is developed is most of the solution. The solving of the equation is just arithmetic with variable x in it. Solve for x.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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 3 hours until Homer had to go home. Mike finished the job working by himself in an additional 3 hours. How long would it have taken Homer to fix the deck himself?
***
let x=hours Homer can do the job alone
1/x=his work rate
x-1=hours Mike can do the job alone
1/(x-1)=his work rate
sum of indv. work rates=work rate working together
1%2Fx%2B1%2F%28x-1%29=%28x-1%2Bx%29%2Fx%28x-1%29=%282x-1%29%2Fx%28x-1%29
..
3 hrs working together+mike working 3 hrs by himself=100% of the job
3(2x-1)/x(x-1)+3(x-1)=1
lcd: x(x-1)
6x-3+3x=x(x-1)
6x-3+3x=x^2-x
x^2-10x+3=0
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=-10, c=3
ans: x≈0.31 (reject)
or
x≈9.7
It will take Homer approximately 9 hours 42 minutes to fix the deck by himself.