Question 713473
<pre>
The filling rate is one tank per 7 minutes or {{{(1_tank)/(7_minutes)}}} or {{{1/7}}}{{{tank/minute}}}.

The emptying rate is NEGATIVE one tank per 10 minutes or {{{-(1_tank)/(10_minutes)}}} or {{{-1/10}}}{{{tank/minute}}}.

So the filling rate when both are open is {{{1/7 - 1/10}}} = {{{10/70- 7/70}}} = {{{3/70}}}{{{(tank)/(minutes)}}} = {{{(3_tanks)/(70_minutes)}}}

Set up a proportion

3 tanks is to 70 minutes as 1 tank is to X minutes

{{{(3_tanks)/(70_minutes)}}}{{{""=""}}}{{{(1_tank)/(X_minutes)}}}

Cross multiply and solve for X.

You'll get that it would take {{{70/3}}} or {{{23&1/3}}} minutes 20 seconds. 

Edwin</pre>