SOLUTION: 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

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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?
Found 2 solutions by scott8148, Edwin McCravy:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
in the 3 hours between 9 and noon , the main pump will empty 3/4 of the tanker (3 hrs / 4 hrs)

this means that the auxiliary pump must empty the remaining 1/4 , it will take the pump 2 ¼ hrs to do this (9 hrs * 1/4)

so the auxiliary must start at 9:45 (2 ¼ hrs before noon)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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?

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