Question 997137
1 POOL, the unit of volume
Oultet at the rate 1/x
Inlet at the rate 1/y
t, time used in filling 1 pool in the step-wise process described


Filling and Emptying in 8 hours
<pre>
          rate       time     quantity
FILL      1/y         t        (1/y)t
EMPTY     1/x        8-t       (1/x)(8-t)
Total                 8         1
</pre>
This gives an equation {{{(1/y)t-(1/x)(8-t)=1}}}.


The fill process with BOTH pipes open gives  {{{(1/y-1/x)=1/7.5}}} and the best you might do is to solve for {{{1/x}}} and substitute into the step-wise equation; but you will still have the UNKNOWN variables of t and y.


Your problem description seem incomplete.  No finished answer.  Maybe another tutor will see a better way.


--
{{{-1/x=1/7.5-1/y}}}
{{{1/x=1/y-1/7.5}}}
-
{{{(1/y)t-(1/y-1/7.5)(8-t)=1}}}
{{{(1/y)t+(1/7.5-1/y)(8-t)=1}}}
{{{(1/y)t+8/7.5-(1/y)8-t/7.5+t/y=1}}}
{{{(1/y)t+8/7.5-8/y-t/7.5+t/y=1}}}, LCD  7.5y;
{{{7.5t+8y-8(7.5)-t*y+7.5t=1}}}
{{{15t+8y-ty-60=1}}}----------still the two unknowns y and t.