.A leak in the bottom of a tank can empty the full tank in 4hours.An inlet pipe fills water at the rate of 5lit a minute.When the tank is full, the inlet is opened and due to the leak,the tank is empty in 6 hours. How many litres does the tank hold?
rate of leak=tank/4 hours
rate of filling=5 lit/min=300lit/hr
net rate=300lit/hr-tank/4hours
volume=0=tank-netrate*6hrs
0=tank-1300lit+tank(4/6)
tank(1-2/3)=1300
tank=3900 liters check that.
To solve this problem, we need to determine the rate at which the leak empties the tank and the rate at which the inlet pipe fills the tank. From there, we can calculate the capacity of the tank.
Let's first determine the rate at which the leak empties the tank. We are given that the leak can empty the full tank in 4 hours. This means that in 1 hour, the leak can empty 1/4th of the tank. We can express this mathematically as:
Leak rate = 1/4 tank/hour
Next, let's determine the rate at which the inlet pipe fills the tank. We are given that the inlet pipe fills water at a rate of 5 liters per minute. To convert this to liters per hour, we can multiply by 60 (since there are 60 minutes in an hour):
Inlet rate = 5 liters/minute * 60 minutes/hour = 300 liters/hour
Now, let's consider the scenario when the tank is full and the inlet pipe is opened. In this scenario, the inlet pipe is filling the tank while the leak is emptying it. We can represent this with the following equation:
Inlet rate - Leak rate = 0 (since the tank is not filling or emptying when it is full)
Substituting the values we calculated:
300 liters/hour - 1/4 tank/hour = 0
To solve for the leak rate, we can multiply both sides of the equation by 4:
4 * (300 liters/hour - 1/4 tank/hour) = 4 * 0
1200 liters/hour - tank/hour = 0
Now, we know that the leak rate is equal to the rate at which the tank empties when it is full. In the scenario where the tank is empty in 6 hours, the leak empties the tank at a rate of 1/6 tank/hour. We can express this mathematically as:
Leak rate = 1/6 tank/hour
Since the leak rate is the same in both scenarios, we can set the two equations equal to each other and solve for the tank capacity:
1200 liters/hour - tank/hour = 1/6 tank/hour
To simplify the equation, we can multiply both sides by 6 to eliminate the fractions:
6 * (1200 liters/hour - tank/hour) = 6 * 1/6 tank/hour
7200 liters - 6 * tank = tank
Adding 6 * tank to both sides of the equation:
7200 liters = 7 * tank
Finally, we can divide both sides by 7 to solve for the tank capacity:
tank = 7200 liters / 7
tank ≈ 1028.57 liters
Therefore, the tank holds approximately 1028.57 liters.