TheNightKing wrote:
kiran120680 wrote:
Water is pumped in and out of a tank using an inlet and outlet pipe respectively. If the tank is initially empty, how much time will it take to fill up the tank, when both the pipes are opened simultaneously?
I. The inlet pipe takes 20 minutes to fill the empty tank and the outlet pipe take 60 minutes to empty a full tank.
II. The amount of water the tank can hold is 100 gallons.
I guess I am not able to think straight because of the person sitting next to me who is continuously talking.
Here is my doubt:
Why is the size of the tank not relevant ?
So Yeah we assume the capacity to be 60 and get inlet pipe work as +3 and outlet as -1 Which gives us a result of 30 minutes. But what if the size of the tank is 600. We get 300 minutes which is 5 hours.
What am I missing?
To see what you missed, work through the full problem with your second example of a size 600 tank.
If the tank has a capacity of 600, then the inlet pipe fills it at a rate of 600 units / 20 minutes = 30 units per minute, and the outlet pipe empties it at a rate of 600 units / 60 minutes = 10 units per minute.
Therefore, the net change is +20 units per minute.
So, to fill the entire thing, it will take 600 units / (20 units per minute) = 30 minutes. That's the same as with a size 60 tank.
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Now, try it with yet another different size tank. What if the size of the tank is 300 instead of 600? The inlet pipe fills 300 units in 20 minutes, so that's 15 units per minute. The outlet pipe empties 300 units in 60 minutes, so that's 5 units per minute. In total, we're at +10 units per minute. Filling the whole thing will take 300 units / (10 units per minute) = 30 minutes. Same value.
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And, with a variable: If the size of the tank is T units, the inlet pipe fills it at T/20 units per minute, and the outlet pipe empties it at T/60 units per minute. The net increase is T/20 - T/60 = 3T/60 - T/60 = 2T/60 = T/30 units per minute.
To fill a tank of size T, at T/30 units per minute, takes T/(T/30) = 30 minutes, no matter what T is. The reason T doesn't matter is that it cancels out in this solution!
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