A tap fills a tank in 6 hours. After half the tank is full, three more identical taps are opened. What is the total time to fill the tank completely?

Problem restatement
First phase: 1 tap until half-full. Second phase: 4 identical taps for the remaining half.

Given data

• Single-tap time = 6 h ⇒ single rate = 1/6 per h

Concept/Approach
Compute phase times separately and add.

Step-by-step calculation
Phase 1: time = (1/2) / (1/6) = 3 hPhase 2: 4 taps ⇒ rate = 4 / 6 = 2/3 per hTime for remaining half = (1/2) / (2/3) = 3/4 h = 45 mTotal time = 3 h + 45 m = 3 h 45 m

Common pitfalls
Averaging rates across phases instead of computing phase-wise times.

Final Answer
3 h 45 m