A tank can be filled by one pump in 3.2 hours and by another pump in 80 minutes. A third pump can drain the tank in 2 hours and 20 minutes. If all 3 pumps go into operation, how long will it take to fill the tank?

Rounding to the nearest minute, it would take 95 minutes, or 1 hour and 35 minutes.

Step-by-step explanation:

Let's convert each time to minutes:

3.2 hours = 192 minutes

80 minutes = 80 minutes

2 hr 20 min = 140 minutes

Next, let's find the least common multiple:

LCM (192, 80, 140) = 6720

So let's say the volume of the tank is 6720 units. The speed of each pump is therefore:

Pump 1 = 6720 units / 192 minutes = 35 units/minute

Pump 2 = 6720 units / 80 minutes = 84 units/minute

Pump 3 = - 6720 units / 140 minutes = - 48 units/minute

Their combined speed is:

35 + 84 - 48 = 71 units/minute

So the time to fill the tank is:

6720 units / (71 units/minute) = 94.65 minutes

Rounding to the nearest minute, it would take 95 minutes, or 1 hour and 35 minutes.