Three pipes with filling and emptying: Pipes A and B can fill a tank in 20 h and 30 h respectively, while pipe C can empty a full tank in 40 h. If all three are opened together on an empty tank, in how many hours will the tank become full?

Introduction / Context:
Multiple pipe problems rely on adding or subtracting rates. Filling pipes contribute positively to the net rate, while an emptying pipe contributes negatively. Once the net hourly fraction of the tank filled is known, the total time is found by taking the reciprocal.

Given Data / Assumptions:

• A fills in 20 h ⇒ rate = 1/20 tank per hour.
• B fills in 30 h ⇒ rate = 1/30 tank per hour.
• C empties in 40 h ⇒ rate = −1/40 tank per hour.
• Tank starts empty; all three are opened together continuously.

Concept / Approach:
Net rate = 1/20 + 1/30 − 1/40. Convert to a common denominator to add/subtract correctly. Time to fill = 1 / (net rate). Mixed fraction form improves readability of the final time.

Step-by-Step Solution:

Verification / Alternative check:
Decimal check: 120/7 ≈ 17.1429 h. A quick sanity check: if the emptying pipe were closed, time would be less than with it open; 120/7 is indeed greater than the combined time of A and B alone (which would be 12 h).

Why Other Options Are Wrong:
16 1/7 h or 18 1/7 h result from arithmetic slips in summing the fractions; 19 1/7 h and 15 h are inconsistent with the computed net rate.

Common Pitfalls:
Adding the emptying rate instead of subtracting it, or using incorrect common denominators for fractional rates. Always standardize denominators before combining rates.

Final Answer:
17 1/7 h