Question 339203
an oil tanker can be emptied by the main pump in four hours. an auxilary pump can empty the tanker in 9 hours. If the main pump started at 9a.m., when should the auxiliary pump be started so the tanker is emptied by noon?
<pre><b>
The main pump's emptying rate is 1/4 tanker per hour.  It will be open
the entire 3 hours, so it will empty 3/4 of the tank.

The other 1/4 of tank must be emptied by the auxiliary pump.

We need to know how long it will take the auxiliary pump to empty
the remaining 1/4 tank which the main pump cannot empty in the
3 hours.

The auxiliary pump's rate is 1/9 tanker per hour.  Let x be the
number of hours it takes the auxiliary pump to empty the 1/4 tank
which the main pump will not be able to empty in the 3 hours allotted.


(rate in tankers per hour)(time required) = 1/4 tank

                                   (1/9)x = 1/4

Multiply both sides by 36

                                       4x = 9
                                        x = 9/4
                                        x = 2 1/4 hours
                                        x = 2 hours 15 minutes

So the auxiliary tank must be started 2 hours 15 minutes before 12 noon,
So it must started at 9:45 AM

Edwin</pre>