Numerical answer
Pipes A and B can fill a tank in 10 minutes and 15 minutes respectively, while pipe C can empty the full tank in 12 minutes. All three pipes are opened together when the tank is empty, and C is closed after 6 minutes. In how many minutes, from the start, will the tank be full?
Show answer and solution
Answer: 9
Net rate with all three open = 1/10 + 1/15 − 1/12. LCM = 60: 6/60 + 4/60 − 5/60 = 5/60 = 1/12 of the tank per minute.
In 6 minutes: 6 × 1/12 = 1/2 of the tank is filled.
After C is closed, A + B fill 1/10 + 1/15 = 1/6 of the tank per minute. The remaining 1/2 takes (1/2) ÷ (1/6) = 3 minutes.
Total time = 6 + 3 = 9 minutes.
Tip: Using LCM (60 units) as the tank capacity: rates 6, 4, −5 units/min; 30 units filled in the first 6 min, remaining 30 units at 10/min takes 3 min.
In 6 minutes: 6 × 1/12 = 1/2 of the tank is filled.
After C is closed, A + B fill 1/10 + 1/15 = 1/6 of the tank per minute. The remaining 1/2 takes (1/2) ÷ (1/6) = 3 minutes.
Total time = 6 + 3 = 9 minutes.
Tip: Using LCM (60 units) as the tank capacity: rates 6, 4, −5 units/min; 30 units filled in the first 6 min, remaining 30 units at 10/min takes 3 min.
Saved on this device. Sign in or create a free account to keep it on every device.