Question 1163951
<br>
Using algebra to solve the problem is good exercise in formal mathematics.  But if a formal solution is not required, the problem is easily solved with logical reasoning and some simple arithmetic.<br>
The main pump is started at 5pm, and the tank is empty at 9pm, so the main pump works for 4 hours.<br>
Since the main pump can empty the entire tank in 5 hours, it does 4/5 of the job of emptying the tank.<br>
So the auxiliary pump has to empty the other 1/5 of the tank.  Since it can empty the entire tank in 11 hours, the time it takes to empty 1/5 of the tank is 11/5 hours, or 2.2 hours, or 2 hours 12 minutes.<br>
So the auxiliary pump must be started 2 hours 12 minutes before 9pm, which is at 6:48pm.<br>