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?

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:
 
 
 it has taken Homer to fix the deck himself about:
 x2 = 11.75 hours