Question 1163951: And oil tanker can be emptied by the main pump in five hours in auxiliary pump can empty the same tanker in 11 hours if the main pump is started at 5 PM when should the auxiliary pump he started so that the tanker is emptied by 9 PM
Found 3 solutions by ikleyn, MathTherapy, greenestamps:
Answer by ikleyn(52756)   (Show Source):
Answer by MathTherapy(10549)  (Show Source):
You can put this solution on YOUR website! And oil tanker can be emptied by the main pump in five hours in auxiliary pump can empty the same tanker in 11 hours if the main pump is started at 5 PM when should the auxiliary pump he started so that the tanker is emptied by 9 PM
Main pump can empty tank in 5 hours, or  of tank in 1 hour
Auxiliary pump can empty tank in 11 hours, or  of tank in 1 hour
Let time it takes auxiliary pump, along, with the main pump, to empty tank, be T
The tank needs to be emptied in 4 hours (5:00 p.m. - 9:00 p.m.), so main pump will be working for 4 hours, while auxiliary will be, for T hours.
We then get the following ENTIRE-JOB equation: 
44 + 5T = 55 ------ Multiplying by LCD, 55
5T = 11
T, or time it takes auxiliary pump, along with main pump, to empty tank = 
Now, subtract that time from 9:00 p.m. to get the time that the auxiliary pump needs to be turned on! Capeesh?
Answer by greenestamps(13196)  (Show Source):
You can put this solution on YOUR website!
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.
The main pump is started at 5pm, and the tank is empty at 9pm, so the main pump works for 4 hours.
Since the main pump can empty the entire tank in 5 hours, it does 4/5 of the job of emptying the tank.
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.
So the auxiliary pump must be started 2 hours 12 minutes before 9pm, which is at 6:48pm.
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