A tank has two inlets that alone would fill it in 40 minutes and 60 minutes, and an outlet that alone would empty a full tank in 48 minutes. All three are opened at a moment when the tank is half full. How long before the tank is full?

Take the tank as 240 units: the inlets give 6 and 4 units a minute, the outlet takes 5, so the net gain is 5 units a minute. Half the tank, 120 units, is still wanted: 120 ÷ 5 = 24 minutes. 48 minutes fills all 240 units at the net rate, forgetting the tank was already half full. 12 minutes uses the right 120 units but ignores the outlet (120 ÷ 10). 8 minutes adds the outlet's 5 units to the inlets instead of subtracting them (120 ÷ 15) — an outlet counts as a negative rate.