Question 889518
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 3 hours. How long would it have taken Homer to fix the deck himself? 
***
let x=hours Homer can do the job alone
1/x=his work rate
x-1=hours Mike can do the job alone
1/(x-1)=his work rate
sum of indv. work rates=work rate working together
{{{1/x+1/(x-1)=(x-1+x)/x(x-1)=(2x-1)/x(x-1)}}}
..
3 hrs working together+mike working 3 hrs by himself=100% of the job
3(2x-1)/x(x-1)+3(x-1)=1
lcd: x(x-1)
6x-3+3x=x(x-1)
6x-3+3x=x^2-x
x^2-10x+3=0
solve for x by quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1, b=-10, c=3
ans: x≈0.31 (reject)
or
x≈9.7 
It will take Homer approximately 9 hours 42 minutes to fix the deck by himself.