Question

The first of three pipes fills a tank in 12 minutes and a second pipe in 10 minutes.If both these pipes and also a third pipe are open, the tank is filled in 4 minutes. How many minute will the third pipe alone require to fill the tank?

Just need an equation.
Thank you!

Answer 1

Let tank volume = V in gallons
First pipe fill rate = Q1 = V/12 g.p.m
Second pipe fill rate = Q2 = V/10 g.p.m
Let Q3 = third pipe fill rate in gallons/min

4 minutes = V/(Q1 + Q2 + Q3)
= V/(V/12 + V/10 + Q3).
= 1/(1/12 + 1/10 + Q3/V)

1/3 + 2/5 + 4 Q3/V = 1
4 Q3/V = 4/15
Q3/V = 1/15
Fill time with pipe 3 alone = V/Q3 = 15 minutes