Time for first half

Since one tap fills the whole tank in 6 hours, it fills half the tank in half that time.

$t_1 = \frac{6}{2} = 3 \text{ hours}$

Rate with additional taps

With one original tap and three additional similar taps, we have a total of 4 taps operating at the same capacity.

$R_{total} = 4 \times R_{tap}$

Time for second half

The time to fill the remaining half of the tank with 4 taps is one-fourth the time a single tap would take to fill half the tank.

$t_2 = \frac{6 \text{ hours}}{4} = 1.5 \text{ hours} = 1 \text{ hour } 30 \text{ minutes}$

Total time calculation

Add the time for the first half and the second half.

$\text{Total} = 3 \text{ hours} + 1 \text{ hour } 30 \text{ minutes} = 4 \text{ hours } 30 \text{ minutes}$