It took approximately 69 minutes for the tank to drain completely when the inlet pipe was left on while draining.
To determine how long it took for the tank to drain completely when the inlet pipe was left on while draining, we need to calculate the net draining rate by considering the rates of both the inlet pipe and the drain.
Given:
Inlet pipe fills the tank in 45 minutes.
Drain empties the tank in 25 minutes.
Let's denote the draining rate as "D," where D is the fraction of the tank drained per minute.
The filling rate of the inlet pipe is 1/45 of the tank per minute, and the draining rate of the drain is 1/25 of the tank per minute.
Therefore, the net draining rate when both pipes are operational is given by:
Net draining rate = Draining rate - Filling rate
Net draining rate = 1/25 - 1/45
To find the time it takes for the tank to drain completely, we set the net draining rate equal to 1 (the entire tank):
1/25 - 1/45 = 1/T
Solving this equation, we find that T is approximately 69 minutes.