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 for the tank to get filled?

One tap can fill the tank in 6 hours.

After half the tank is filled, 3 more similar taps are opened.

Total work = Efficiency × time  

Solution: 

Let the capacity of the tank be 6 unit,

So, Efficiency of the one tap = $$\frac{6}{6} = 1 \, unit/hour$$ 

Time taken to fill the half tank = $$\frac{3}{1} = 3 \, hours$$ 

Now, 3 more taps are opened, 

total taps working = 1 + 3 = 4 

total efficiency of 4 taps = $$4 \times 1 = 4 \, unit/hours$$ 

remaining tank to be filled by 4 taps,

time taken = $$\frac{3}{4} = \frac{3 \times 60}{4} = 45 \, minutes$$ 

Thus, total time taken to fill the full tank = 3hours + 45 minutes = 3 hours 45 minutes