A pipe can fill an empty tank in 10 hours, while another pipe can empty the…
2026
A pipe can fill an empty tank in 10 hours, while another pipe can empty the filled tank in 20 hours. If both pipes are opened simultaneously when the tank is empty, how many hours will it take for the tank to be three-fourths full?
Answer: B. 15 — Concept: Every pipe works at a steady rate equal to one tankful divided by the time it needs on its own. An inlet counts as a positive rate and an outlet as a…
- A.
45
- B.
15
- C.
30
- D.
60
Attempted by 48 students.
Show answer & explanation
Correct answer: B
Concept: Every pipe works at a steady rate equal to one tankful divided by the time it needs on its own. An inlet counts as a positive rate and an outlet as a negative one, and pipes that run at the same time simply add their rates. The time needed to reach any required part of the tank is that required part divided by the combined rate.
Applying this to the given tank:
Inlet pipe: it fills 1 tank in 10 hours, so its rate is 1/10 tank per hour.
Outlet pipe: it empties 1 tank in 20 hours, so its rate is -1/20 tank per hour.
Both are open together from the start, so the combined rate is 1/10 - 1/20 = 2/20 - 1/20 = 1/20 tank per hour. This is positive, so the water level does rise.
The part of the tank that has to be reached is 3/4 of a tankful.
Time = required part / combined rate = (3/4) / (1/20) = (3/4) x 20 = 15 hours.
Cross-check: In 15 hours the inlet by itself pours in 15/10 = 1.5 tankfuls and the outlet by itself drains 15/20 = 0.75 tankful, so the water standing in the tank is 1.5 - 0.75 = 0.75 tankful, which is three-fourths of the tank, exactly as required.
Always check the sign of the combined rate before dividing: if the outlet were the faster pipe the combined rate would be negative and the tank started empty would never fill at all.