A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Let's assume the capacity of the tank is 60 units.

A tap can fill the tank in 6 hours. The rate at which this tap fills is $$\frac{60}{6}$$ = 10 units/ hr.

The time this tap takes to fill half the tank is $$\frac{6}{2}=3 hrs$$

Now, 3 more similar taps are opened, so there are 4 taps running at a rate of 10 units/hr.

The rate of all four taps combined is 40 units/hr.

The time taken by these four taps to fill 30 units is $$\frac{30}{40}$$ = $$\frac{3}{4}$$hr  =45 mins.

The total time taken is 3 hrs 45 mins.