Question 981128: A tap can fill the tank in 16 minutes and another can empty in 8 minutes.If the tank is already half full and both the taps are opened together,the tank will be:
a. Filled in 12 minutes
b. Emptied in 12 min
c. Filled in 8 min
d emptied in 8 min
e. None of above
Found 2 solutions by Edwin McCravy, macston:
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
Instead of doing your problem, I'll do one exactly like it with different
numbers.
A tap can fill the tank in 15 minutes and another can empty in 6 minutes. If the
tank is already half full and both the taps are opened together,the tank will be:
The filling tap's rate is 1/15 of a tank per minute.
The emptying tap's rate is 1/6 of a tank per minute, which we interpret as a
negative filling rate, that is, a filling rate of -1/6 tankj per minute.
Therefore the combined rate of both taps is 1/15-1/6 = 2/30-5/30 = -3/30 or
-1/10 tank per minute. So we know the tank will be empty, since the combined
filling rate is negative. So we use the formula
TIME = (part of tank to fill, which is negative)/rate
TIME = (-1/2)/(-1/10) = (-1/2)(-10/1) = 5 minutes to empty it.
Now, you can use this as a model to solve your problem.
Edwin
Answer by macston(5194)  (Show Source):
You can put this solution on YOUR website! .
fill tap=1 tank/16 min=1/16 tank/min
empty tap=-1tank/8 min=-1/8 tank/min
Together=1/16 tank/min-1/8 tank/min=-1/16 tank min
.
With both valves open, 1/16 of the tank will empty per minute.
Since 1/2 (8/16) of the tank is full at the start, it will take (8/16 tank/(1/16 tank/min)) 8 minutes for the tank to empty.
.
Correct answer is D. emptied in 8 minutes.
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