A pipe can fill a tank in 12 hours. Another pipe can empty the filled tank in…
2026
A pipe can fill a tank in 12 hours. Another pipe can empty the filled tank in 24 hours. If both pipes are opened simultaneously, in how many hours will the tank be filled?
Answer: D. 24 — Concept. When one pipe fills a tank and another empties it at the same time, their rates act in opposite directions. If a pipe fills the tank in a hours, its…
- A.
25
- B.
26
- C.
27
- D.
24
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Show answer & explanation
Correct answer: D
Concept. When one pipe fills a tank and another empties it at the same time, their rates act in opposite directions.
If a pipe fills the tank in a hours, its rate is 1/a tank per hour; if another empties it in b hours, its rate is -1/b tank per hour.
Application. Use the net-rate rule for the two simultaneous flows.
The filling rate is 1/12 tank per hour, and the emptying rate is 1/24 tank per hour.
Therefore, the net filling rate is 1/12 - 1/24 = 2/24 - 1/24 = 1/24 tank per hour.
Time to fill one tank = 1 ÷ (1/24) = 24 hours.
Cross-check. In 24 hours, the inlet fills 24/12 = 2 tanks, while the outlet removes 24/24 = 1 tank. The net amount filled is 2 - 1 = 1 tank.
Result. Thus, the tank is filled in 24 hours.