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Two pipes feed a water tank at the rate ...

Two pipes feed a water tank at the rate os 2 litres/minutes and 3 litre/minute. A third pipe draws out water at a rate of 6 litres/minute. The capacity of the tank is 100 litres and its full of water. How many minutes would it takes to make the tank empty if three pipes are opened simultaneously?

A

125

B

75

C

100

D

50

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to calculate the net rate at which water is being emptied from the tank when all three pipes are opened simultaneously. ### Step-by-Step Solution: 1. **Identify the rates of the pipes:** - Pipe A fills water at a rate of 2 litres/minute. - Pipe B fills water at a rate of 3 litres/minute. - Pipe C draws out water at a rate of 6 litres/minute. 2. **Calculate the total filling rate:** - Total filling rate from pipes A and B: \[ \text{Total filling rate} = 2 \text{ litres/min} + 3 \text{ litres/min} = 5 \text{ litres/min} \] 3. **Calculate the net rate of water in the tank:** - Since Pipe C is drawing water out, we need to subtract its rate from the total filling rate: \[ \text{Net rate} = \text{Total filling rate} - \text{Rate of Pipe C} = 5 \text{ litres/min} - 6 \text{ litres/min} = -1 \text{ litre/min} \] - This means that the tank is emptying at a rate of 1 litre per minute. 4. **Determine the time to empty the tank:** - The capacity of the tank is 100 litres. To find out how long it will take to empty the tank at the net rate of -1 litre/min: \[ \text{Time to empty} = \frac{\text{Total volume}}{\text{Net rate}} = \frac{100 \text{ litres}}{1 \text{ litre/min}} = 100 \text{ minutes} \] ### Final Answer: It will take **100 minutes** to empty the tank when all three pipes are opened simultaneously.
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