Question

It takes 3 minutes to fill an empty tank with water from a tap. When the tap is turned off and the drain is opened, it takes 4 minutes for the tank to empty. If the tap is turned on and the drain is opened at the same time, how long will it take to fill the empty tank?

Answer 1

When the tap is turned on and the drain is opened at the same time, it will take 12 minutes to fill the empty tank.

Step-by-step explanation:

To determine how long it will take to fill the empty tank when the tap is turned on and the drain is opened at the same time, we need to consider the inflow rate and the outflow rate.

Given that it takes 3 minutes to fill the tank and 4 minutes to empty it, we can find the rates:

Inflow rate: 1 tank / 3 minutes = 1/3 tanks per minute

Outflow rate: 1 tank / 4 minutes = 1/4 tanks per minute

When both the tap and the drain are open, the effective inflow rate is reduced by the outflow rate:

Effective inflow rate = Inflow rate - Outflow rate = 1/3 - 1/4 = 1/12 tanks per minute

Therefore, it will take 12 minutes to fill the empty tank when the tap is turned on and the drain is opened at the same time.