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?

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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:    Mike finished the job working by himself in an additional 5 hours:    From here, we must clear the value of x.  We then have to multiply both sides by x (x-1):    Rewriting we have:    The solutions to the equation are:    Answer:  it has taken Homer to fix the deck himself about:  x2 = 11.75 hours


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