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jolli1 [7]
3 years ago
15

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 wor

ked 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?
Mathematics
1 answer:
DiKsa [7]3 years ago
5 0
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  \frac{1}{x} + 3  \frac{1}{x-1}
 Mike finished the job working by himself in an additional 5 hours:
 3  \frac{1}{x} + 3  \frac{1}{x-1} + 5 \frac{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
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