Question 1113669
{{{FastPipe+SlowPipe=BothPipesTogether}}}


{{{1/x+1/(x+5)=1/5}}}


LCD {{{5x(x+5)}}}


{{{5(x+5)+5x=x(x+5)}}}

{{{5x+25+5x=x^2+5x}}}

{{{5x+25=x^2}}}

{{{x^2-5x-25=0}}}

{{{x=(5+- sqrt(25-4(-25)))/2}}}

{{{x=(5+- sqrt(125))/2}}}

{{{x=(5+5*sqrt(5))/2}}}

{{{x=8.090}}}


Ignoring the small fraction part of x,  
The fast pipe would take  8 hours and the slow pipe would take 13 hours.