# 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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carlosegoFor 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