Pipes A, B, and C together fill a tank in 6 hours. After 2 hours, C is closed and A & B fill the rest in 7 hours. How many hours would C alone take to fill the tank?

Problem restatement
All three fill for 2 hours, then only A and B continue for 7 hours. Find C's solo time.

Given data

• a + b + c = 1/6 (tank per hour)
• Work done in first 2 hours = 2 / 6 = 1/3
• Remaining = 2/3 done by A + B in 7 hours ⇒ a + b = 2/21

Concept/Approach
Subtract to get c: c = (1/6) − (2/21). Then invert to get time.

Step-by-step calculation
c = 1/6 − 2/21 = 7/42 − 4/42 = 3/42 = 1/14So C's time = 14 hours

Verification/Alternative
Rates: a + b = 2/21; with c = 1/14 ⇒ a + b + c = 2/21 + 1/14 = 4/42 + 3/42 = 1/6.

Common pitfalls
Using 2 hours of A and B instead of 7 hours when setting a + b; mixing hours and fractions.

Final Answer
14 hours