There are five containers A, B, C, D and E each containing 1200 litres of water. The water is beingpumped from one tank to another as follows:From A to B at 30 litres/minuteFrom C to A at 60 litres/minuteFrom A to E at 20 litres/minuteFrom C to D at 50 litres/minuteFrom D to B at 80 litres/minuteFrom B to C at 60 litres/minuteFrom E to D at 10 litres/minuteFrom E to A at 10 litres/minuteWhich tank gets emptied first?
Question
There are five containers A, B, C, D and E each containing 1200 litres of water. The water is beingpumped from one tank to another as follows:From A to B at 30 litres/minuteFrom C to A at 60 litres/minuteFrom A to E at 20 litres/minuteFrom C to D at 50 litres/minuteFrom D to B at 80 litres/minuteFrom B to C at 60 litres/minuteFrom E to D at 10 litres/minuteFrom E to A at 10 litres/minuteWhich tank gets emptied first?
Solution
To determine which tank gets emptied first, we need to calculate the net flow of water in and out of each tank per minute.
Let's start with tank A:
- Water is pumped from C to A at a rate of 60 litres/minute.
- Water is pumped from A to B at a rate of 30 litres/minute.
- Water is pumped from A to E at a rate of 20 litres/minute.
- Water is pumped from E to A at a rate of 10 litres/minute.
The net flow of water into tank A per minute is: 60 - 30 - 20 + 10 = 20 litres/minute.
Moving on to tank B:
- Water is pumped from A to B at a rate of 30 litres/minute.
- Water is pumped from D to B at a rate of 80 litres/minute.
- Water is pumped from B to C at a rate of 60 litres/minute.
The net flow of water into tank B per minute is: 30 + 80 - 60 = 50 litres/minute.
Next is tank C:
- Water is pumped from C to A at a rate of 60 litres/minute.
- Water is pumped from B to C at a rate of 60 litres/minute.
The net flow of water into tank C per minute is: 60 - 60 = 0 litres/minute.
Moving on to tank D:
- Water is pumped from C to D at a rate of 50 litres/minute.
- Water is pumped from E to D at a rate of 10 litres/minute.
The net flow of water into tank D per minute is: 50 + 10 = 60 litres/minute.
Lastly, tank E:
- Water is pumped from A to E at a rate of 20 litres/minute.
- Water is pumped from E to D at a rate of 10 litres/minute.
- Water is pumped from E to A at a rate of 10 litres/minute.
The net flow of water into tank E per minute is: 20 - 10 - 10 = 0 litres/minute.
Based on the net flow rates, we can see that tank C has a net flow of 0 litres/minute, meaning no water is entering or leaving the tank. Therefore, tank C will be the first to get emptied.
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