Two pipes, A and B, can fill a tank in 8 minutes and 10 minutes, respectively.…
2026
Two pipes, A and B, can fill a tank in 8 minutes and 10 minutes, respectively. Both pipes start filling the tank together, but after 4 minutes, they stop due to a technical issue. The remaining portion of the tank is then filled by a third pipe, C, which alone can fill the tank in 12 minutes. How long will pipe C take to fill the remaining part of the tank?
Answer: B. 1.2 min — ConceptWhen a pipe fills a tank in T minutes, its filling rate is 1/T tank per minute. Rates of pipes working together are added. Work completed equals…
- A.
2.5 min
- B.
1.2 min
- C.
4.2 min
- D.
3.1 min
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Show answer & explanation
Correct answer: B
Concept
When a pipe fills a tank in T minutes, its filling rate is 1/T tank per minute. Rates of pipes working together are added.
Work completed equals combined rate multiplied by time. The time for a later pipe equals the remaining fraction divided by that pipe’s rate.
Application
Pipe A’s rate is 1/8 tank per minute, and pipe B’s rate is 1/10 tank per minute.
Their combined rate is 1/8 + 1/10 = 5/40 + 4/40 = 9/40 tank per minute.
In 4 minutes, A and B fill 4 × 9/40 = 36/40 = 9/10 of the tank.
The remaining fraction is 1 − 9/10 = 1/10 of the tank.
Pipe C’s rate is 1/12 tank per minute, so its required time is (1/10) ÷ (1/12) = 12/10 = 1.2 minutes.
Cross-check
In 1.2 minutes, pipe C fills 1.2 × 1/12 = 0.1 = 1/10 of the tank, exactly the remaining portion.
Therefore, pipe C takes 1.2 minutes.