A tank is filled by one tap in 20 minutes and by another in 25 minutes. If both tapes are kept open for 5 minutes and then the second is turned off. In how many minutes the tank will be completely filled?
Answer: 11 minutes
Explanation
Let's calculate the work done by both taps in 5 minutes:
Tap 1 fills the tank in 20 minutes, so in 1 minute it fills 1/20 of the tank. In 5 minutes, it fills 5/20 = 1/4 of the tank.
Tap 2 fills the tank in 25 minutes, so in 1 minute it fills 1/25 of the tank. In 5 minutes, it fills 5/25 = 1/5 of the tank.
Combined work in 5 minutes = 1/4 + 1/5 = (5 + 4)/20 = 9/20
Work left = 1 - 9/20 = 11/20
Now, Tap 1 fills 1/20 of the tank in 1 minute. To fill 11/20 of the tank, it will take:
(11/20) / (1/20) = 11 minutes
