Ratio proportion

Question

There are three pipes A,B & C which can fill empty tank in 30 min, 20 min, and 10 min. All three pipes are opened and the pipes discharge chemical P, Q & R. What is the proportion of solution P, Q & R in the liquid in the tank after 3 min?

Answer 1

Let me begin by saying that it was very naughty of you for getting us to do your homework. But because you are a new user, I have decided I will post this to help you just this once:

Let x be the rate at which water exits pipe C. (volume/time)
Let y be the rate at which water exits pipe B.
let z be the rate at which water exits pipe A.

From the above information, we can deduce that x = 3z. This is because a fixed volume is filled in 1/3 time when pipe C is used than when pipe A is used. Since Rate has time on the denominator, the rate water exits pipe C must be 3 times faster than pipe A.

Similarly, y = 1.5z.

If all pipes are oppened at once, water enters the system at a rate equal to:
x + y + z = 3z + 1.5z + z = 5.5z.

Therefore, proportion of liquid from pipe A = z/5.5z = 1/5.5
proportion of liquid from pipe B = 1.5z/5.5z = 1.5/5.5
proportion of liquid from pipe C = 3z/5.5z = 3/5.5