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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 5 hours. How long would it have taken Homer to fix the deck​ himself?

User Dollie
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1 Answer

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For this case, the first thing we are going to do is define variables.
We have then:
x: number of hours it takes Homer to finish work alone.
They worked together for 3 hours until Homer had to go home:

3 (1)/(x) + 3 (1)/(x-1)
Mike finished the job working by himself in an additional 5 hours:

3 (1)/(x) + 3 (1)/(x-1) + 5 (1)/(x-1) = 1
From here, we must clear the value of x.
We then have to multiply both sides by x (x-1):

3 (x-1) + 3x + 5x = x (x-1)
Rewriting we have:

3x - 3 + 3x + 5x = x ^ 2 - x x ^ 2 - 12x + 3 = 0
The solutions to the equation are:

x1 = 0.25 (discarded) x2 = 11.75
Answer:
it has taken Homer to fix the deck himself about:
x2 = 11.75 hours
User LaytonGB
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