Three pipes A, B and C can fill a tank in 12 hours, 15 hours and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, in how many hours will the tank be full?
Three pipes A, B and C can fill a tank in 12 hours, 15 hours and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, in how many hours will the tank be full?
Solution
Pipe A fills the tank in 12 hours, so in 1 hour it fills of the tank.
Pipe B fills the tank in 15 hours, so in 1 hour it fills of the tank.
Pipe C fills the tank in 20 hours, so in 1 hour it fills of the tank.
Pipe A is always working. Pipes B and C work alternately for 1 hour each.
The pattern is:
- Hour 1: A + B working together
- Hour 2: A + C working together
- Hour 3: A + B working together
- Hour 4: A + C working together
In Hour 1, when A and B work together:
Work done
of tank filled
In Hour 2, when A and C work together:
Work done
of tank filled
In 2 hours (one complete cycle):
Work done
of tank filled
After 6 hours (3 complete cycles):
Work done
of tank filled
Remaining work
of tank
In the 7th hour, A and B work together.
Work done of tank
This exactly equals the remaining work, so the tank is completely full after 7 hours.