Question

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?

• A. 4 hours
• B. 5 hours
• C. 3 hours 30 minutes
• D. 3 hours 45 minutes

Answer 1

The Correct Option is D

A tap can fill a tank in 6 hours, so it fills \(\frac{1}{6}\) of the tank in one hour.

After half the tank is filled, it takes \(\frac{1}{2} \times 6 = 3\) hours.

Three more similar taps are opened, so now there are a total of 4 taps. Each tap fills \(\frac{1}{6}\) of the tank per hour, so the four taps together fill \(4 \times \frac{1}{6} = \frac{4}{6} = \frac{2}{3}\) of the tank per hour.

The remaining half of the tank needs to be filled. 

The time it takes for the 4 taps to fill the remaining half is \(\frac{1/2}{2/3} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}\) hours, which is 45 minutes.

The total time taken to fill the tank completely is 3 hours + 45 minutes = 3 hours 45 minutes.

Answer 2

The first tap fills half the tank in 3 hours. 

After that, four taps are opened, so the remaining half is filled at four times the rate: 

Time to fill the remaining half = $\frac{3}{4} = 0.75$ hours. 

Total time = 3 + 0.75 = 3.75 hours = 3 hours 45 minutes.