Question 886043
<pre>
A tank is filled in 9 hrs. 

So the fill rate is 1 tank per 9 hrs or

{{{matrix(1,2,1,tank)/matrix(1,2,9,hrs)}}} or {{{matrix(1,2,1/9,tank/hr)}}},

and the drain rate is -1 tank per 11 hrs or

{{{matrix(1,2,-1,tank)/matrix(1,2,11,hrs)}}} or {{{matrix(1,2,-1/11,tank/hr)}}}.

Since the drain is only half open, it's rate is halved

{{{matrix(1,2,expr(1/2)*(-1/11),tank/hr)}}} or {{{matrix(1,2,-1/22,tank/hr)}}}

Their combined rate is {{{matrix(1,2,1/9-1/22,tank/hr)}}} or

since {{{1/9-1/22=22/198-9/198=13/198}}}

their combined fill rate is {{{matrix(1,2,13/198,tank/hr)}}}

Suppose it takes x hours.  Then

{{{matrix(1,2,13/198,tank/hr)}}}{{{""*""}}}{{{matrix(1,2,x,hr)}}} {{{""=""}}} {{{matrix(1,2,1,tank)}}}

{{{expr(13/198)*x}}}{{{""=""}}}{{{1}}}

{{{x}}}{{{""=""}}}{{{198/13}}}{{{""=""}}}{{{matrix(1,2,15&3/13,hours)}}} 

Edwin</pre>