Early filling, then steady emptying (clarified timing) Pipe P fills in 12 min and pipe R fills in 15 min, while pipe M empties in 6 min. First, only P and R run for 5 min (twice 2.5 min, as intended). Then M is also opened. After how much time <em>from the moment M is opened</em> will the tank be empty?

Introduction / Context:
The original stem was ambiguous about whether “emptied” is measured from the start or from adding the outlet. By the Recovery-First Policy, we clarify that the asked time is after opening the outlet, which aligns with the given options and preserves the core intent.

Given Data / Assumptions:

• P: 12 min ⇒ 1/12 per min.
• R: 15 min ⇒ 1/15 per min.
• M (outlet): 6 min ⇒ 1/6 per min (negative in net).
• Phase 1: P+R for 5 min.
• Phase 2: P+R+M thereafter.

Concept / Approach:
Compute the volume after Phase 1, then the net emptying rate in Phase 2. Time to empty equals volume / rate.

Step-by-Step Solution:

Verification / Alternative check:
Total elapsed from the very start would be 5 + 45 = 50 min, but the clarified question asks the duration after M is opened.

Why Other Options Are Wrong:
50 min is the start-to-empty duration; 25 and 35 are inconsistent with the computed net rate.

Common Pitfalls:
Trying to “average times” instead of using rates, or forgetting sign when an outlet is added.

Final Answer:
45 min