Two pipes A and B can fill a tank in 15 min and 20 min. Both are opened; after 4 min, A is closed. What is the total time to fill the tank?

Problem restatementPipes A and B run together for 4 minutes, then only B continues. Find total filling time.

Given data

• A's rate = 1/15 tank/min; B's rate = 1/20 tank/min.
• Both open for first 4 min, then only B runs.

Concept/ApproachCompute work done in the first phase, subtract from 1 tank, then compute remaining time with B alone.

Step-by-step calculation Rate(A + B) = 1/15 + 1/20 = 7/60 tank/min Work in 4 min = 4 × 7/60 = 28/60 = 7/15 tank Remaining = 1 − 7/15 = 8/15 tank Time with B alone = (8/15) ÷ (1/20) = (8/15) × 20 = 160/15 = 10 2/3 min = 10 min 40 s Total time = 4 min + 10 min 40 s = 14 min 40 s

Verification/AlternativeFractional minutes 10 2/3 converts to 10 minutes 40 seconds (since 2/3 of a minute is 40 seconds).

Common pitfalls

• Using A's time after closing instead of B's.
• Arithmetic slip when converting fractional minutes to seconds.

Final Answer14 minutes 40 seconds