a water tank gets fully filled in by inlet pipe in 3 hours. and it gets totally empty out by an outlet pipe in 5 hours. if we keep both the pipes open ho much time it will take to fill in the tank fully?
1/t = 1/3 - 1/5
now solve for t.
To determine the time it will take to fill the tank when both the inlet and outlet pipes are open, we can calculate the rate at which each pipe fills or empties the tank.
Let's assume that the total capacity of the tank is V liters (you can replace V with any desired value).
We are given:
- The inlet pipe fills the tank in 3 hours, so the rate of filling is V liters/3 hours.
- The outlet pipe empties the tank in 5 hours, so the rate of emptying is V liters/5 hours.
Now, when both pipes are open, we need to find the net rate of filling. This can be determined by subtracting the rate of emptying from the rate of filling:
Net rate = Filling rate - Emptying rate
= V/3 - V/5
= (5V - 3V) / 15
= 2V / 15 liters per hour
Therefore, when both pipes are open, the tank fills at a rate of 2V / 15 liters per hour.
To find the time it takes to fill the tank, we can divide the total capacity (V) by the rate of filling when both pipes are open:
Time to fill = Total capacity / Filling rate
= V / (2V / 15)
= 15 / 2 hours
= 7.5 hours
So, when both the inlet and outlet pipes are open, it will take 7.5 hours to fully fill the tank.