Question 313795
Let x = time it will take for all three sources to fill the reservoir.


In 1 hour, source A can fill 1/2 of it, source B can fill 1/3 of it, source C can fill 1/6 of it, and all sources together can fill 1/x of it.  The equation is:


{{{1/2 +1/3 +1/6=1/x}}}


Multiply both sides by 6x:
{{{(6x)*(1/2)+(6x)*(1/3)+(6x)*(1/6)=(6x)*(1/x)}}}
{{{3x +2x +x=6}}}
{{{6x=6}}}
{{{x=1}}} hour to fill with all sources.


Dr. Robert J. Rapalje, Retired