pipes and cistern

Question

Pipes A & B can fill the tank in 30m & 20m respectively and C can empty it in 15m. All are open alternatively for 1m each.

How much time will be taken to fill the tank?

Answer 1

1/30 + 1/20 - 1/15 in three minutes

LCD:

2/60 + 3/60 - 4/60 in three minutes

simplify:

1/60 in three minutes

 

So after three minutes, the cistern is 1/60 full

Let's look at what happens after 55 intervals of 3 minutes. we're at 55/60 full.

55/60 + 2/60 (pipe A) = 57/60

57/60 + 3/60 (pipe B) = 60/60

 

So we have 55 intervals of three minutes plus two more minutes.

55 * 3 + 2 = __

165 + 2 = 167 minutes

 

 

Answer 2

In the first round (1 m each)

1/30 + 1/20 - 1/15

2/60 + 3/60 - 4/60

1/60

In the 3 m 1/60 is filled.

Therefore the tank fills in

3 (60) or 180 m