Question 898080
The rates for each pipe:
1/x
1/(x+3)
Both at same time:
{{{1/x+1/(x+3)=(x+3+x)/(x(x+3))=highlight_green((2x+3)/(x(x+3)))}}}.


Both together do the job in 2 hours.
{{{highlight_green((2x+3)/(x(x+3))=1/2)}}}
{{{2x+3=(x^2+3x)/2}}}
{{{2(2x+3)=x^2+3x}}}
{{{4x+6=x^2+3x}}}
{{{x+6=x^2}}}
{{{x^2-x-6=0}}}
{{{(x+2)(x-3)=0}}}


The solution which makes sense is {{{highlight(highlight(x=3))}}}.
First pipe would take 3 hours;
Second pipe alone would take 6 hours.