Homer and Mike were replacing on mikes old deck. Mike can do the job in one hour less than Homer. they worked together for three hours until Homer had to go home. Mike finished the job working by himself for an additional 4 hours. How long would it have taken Homer to finish the deck by himself

Let h = time (hours) it takes Homer to do it himself

then

h-1 = time (hours) it takes Mike to do the job alone

3(1/h + 1/(h-1)) + 4(1/(h-1)) = 1

multiplying both sides by h(h-1):

3(h-1 + h) + 4h = h(h-1)

3(2h-1) + 4h = h^2-h

6h-3 + 4h = h^2-h

-3 + 10h = h^2-h

10h = h^2-h+3

0 = h^2-11h+3

applying the quadratic formula yields:

h = {10.72, 0.28}

throw out the .28 (extraneous) leaving

h = 10.72 hours

or

h = 10 hours and 43 minutes