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?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3 hours 45 minutes
A tap that fills the tank in 6 hours fills \(\frac{1}{6}\) of it in one hour, and taps working together add their hourly work. The filling is done in two stages: one tap for the first half, four taps for the second half.
First half, one tap:
Time \(\displaystyle =\frac{1}{2}\div\frac{1}{6}=3\) hours
Second half, four taps (the first tap and three more):
Work of four taps in one hour \(\displaystyle =4\times\frac{1}{6}=\frac{2}{3}\) of the tank
Time \(\displaystyle =\frac{1}{2}\div\frac{2}{3}=\frac{3}{4}\) hour \(=45\) minutes
Total time \(=3\) hours \(+\) 45 minutes \(=\) 3 hours 45 minutes.