Pipes A and B fill a tank in 5 h and 6 h; pipe C empties it in 12 h. If all three are opened together, how long will the tank take to fill?

Problem restatement
Combine two inlet rates and one outlet rate to get net fill time.

Given data

• A = 1/5 per h
• B = 1/6 per h
• C (outlet) = 1/12 per h

Concept/Approach
Net rate = A + B − C. Time = 1 / (net rate).

Step-by-step calculation
Net rate = 1/5 + 1/6 − 1/12= (12 + 10 − 5)/60 = 17/60 per hourTime = 1 / (17/60) = 60/17 hours = 3 9/17 hours ≈ 3 h 31 m 46 s

Verification/Alternative
Check net positivity: 1/5 + 1/6 > 1/12, so the tank fills.

Common pitfalls
Adding times instead of rates, or subtracting 1/12 from only one inlet.

Final Answer
3 9/17 hours (≈ 3 h 31 m 46 s)