three pipes A ,B and C can fill a tank in 10 minutes, 15 mins, and 30 mins respectively. what is the time taken by three pipes to fill the tank if they are opened together?
Answers
Pipe A = 1/15 tank per minute or 4 tanks / hour
Pipe B = 1/20 tank per minute or 3 tanks / hour
Pipe C = 1/30 tank per minute or 2 tanks / hour
So if x is the number of minutes all 3 pipes are running…
((1/15 + 1/20 + 1/30) * x) + ((1/15 + 1/20) * 6) = 1 tank
((1/15 + 1/20 + 1/30) * x) + (7/60) * 6 = 1
((1/15 + 1/20 + 1/30) * x) + .7 = 1
Pipe A + Pipe B fill the tank at a combined rate of 7 tanks per 60 minutes, so in the last 6 minutes they fill up 7/10 of the tank.
((1/15 + 1/20 + 1/30) * x) = .3
So that means that only 1 - 7/10 of the tank, or 3/10 was filled up when all 3 were running.
(1/15 + 1/20 + 1/30) * x = .3
9/60 * x = .3
With all 3 running = 9 tanks / 60 minutes
x = .3 / (9/60)
x = 2 minutes
So let’s confirm, all 3 pipes run for 2 minutes, then just A + B run for 6 minutes,
((1/15 + 1/20 + 1/30) * 2) + ((1/15 + 1/20) * 6) = 1 tank
2 minutes + 6 minutes = 8 minutes total to fill the tank