A tap can fill a tank in 6 hours . After half the tank is filled another simila tap is opened. What is the total time taken to fill the tank completely?

Let's calculate the rate at which the first tap can fill the tank in 1 hour:

First tap's rate = 1 tank / 6 hours = 1/6 tanks per hour

Now, when half of the tank is filled, it means that 1/2 of the tank is filled. So, we have 1/2 of the tank remaining to be filled.

Now, both the first tap and the second tap are open, and they are filling the tank simultaneously. The combined rate at which they can fill the tank is the sum of their individual rates.

Combined rate = (Rate of first tap) + (Rate of second tap)

Since both taps are identical, we can add the rates:

Combined rate = (1/6 + 1/6) tanks per hour = 2/6 tanks per hour = 1/3 tanks per hour

Now, we need to find out how long it will take to fill the remaining 1/2 of the tank at this combined rate:

Time = (Amount remaining to be filled) / (Combined rate)

Time = (1/2 tank) / (1/3 tanks per hour)

Time = (1/2) / (1/3) hours

Time = (1/2) * (3/1) hours

Time = 3/2 hours

Now, convert 3/2 hours into hours and minutes:

3/2 hours = 1 hour and 30 minutes

So, it will take 1 hour and 30 minutes to fill the remaining half of the tank when both taps are open.

Now, let's add this time to the initial 3 hours (time to fill the first half of the tank):

Total time = 3 hours (first half) + 1 hour 30 minutes (remaining half)

Total time = 3 hours + 1 hour 30 minutes

Total time = 4 hours and 30 minutes

So, the total time taken to fill the tank completely is 4 hours and 30 minutes.