# Calculate time to fill an empty tank

An empty tank can be filled with water in 20 minutes by using Pipe A or in 30 minutes by Pipe B, and the tank filled with water can be emptied of water in 40 minutes by using Pipe C. When the three pipes A, B, and C work together, approximately how long (in minutes) does it take to fill the empty tank with water?

I would love to know the method to solve this kind of math. Thanks lot!

• I would suggest graphing the problem first, that usually helps. What have you done so far? Oct 20, 2014 at 15:02
• The flow rate is volume/time (how much do you fill in one minute). The good thing you can add and substract flow rates, it acts like speed. Any idea? Oct 20, 2014 at 15:05
• @Mattos: I've been thinking about this all day! Couldn't try anything! Oct 20, 2014 at 15:10

It's all about placing the information into a formula:

Pipe A fills the tank in 20 minutes, so every minute it fills $\frac{1}{20}$ of the tank.

Pipe B fills the tank in 30 minutes, so every minute it fills $\frac{1}{30}$ of the tank.

Pipe C empties the tank in 40 minutes, so every minute it empties $\frac{1}{40}$ of the tank.

The volume of the tank is equal to $\frac{1}{20}t+\frac{1}{30}t-\frac{1}{40}t$, with $t$ in minutes. The tank is full when the equation is equal to 1. So the equation to solve is $\frac{1}{20}t+\frac{1}{30}t-\frac{1}{40}t = 1$. I think you can take it over from here.

• The way you answer is very easy to understand. And I also misunderstood the question, I thought pipe C will be used to fill the water in the tank too. Anyway, great answer! Oct 20, 2014 at 15:13

Observe a single minute:

• $\dfrac{1}{20}$ of the tank is filled using pipe A
• $\dfrac{1}{30}$ of the tank is filled using pipe B
• $\dfrac{1}{40}$ of the tank is emptied using pipe C

So in a single minute, $\dfrac{1}{20}+\dfrac{1}{30}-\dfrac{1}{40}=\dfrac{7}{120}$ of the tank is filled.

Hence, the entire tank will be filled within $\dfrac{120}{7}$ minutes ($17$ minutes and ~$8.5$ seconds).

Hint: Find the flow rate for each pipe, in "tanks per minute." You'll be gaining a certain amount of tanks per minute from pipes A and B, losing a certain amount from pipe C. So, what is the net amount of tanks per minute? What can we then conclude?

• Thanks! I totally understand now! Oct 20, 2014 at 15:13

Efficiency method

Pipe A , B , -C Time 20 , 30 , 40

Lcm : 120

Efficiency 6 (120/20) , 4(120/30) , -3 (120/40)

Total capacity of tank = 120 litre (lcm)

A= fill 6 part per min, B = fill 4 part per min, C = empty 3 part per min

A,B,C opened together = A+B-C =6+4-3= fill 7 part per min.. So, time taken to fill the tank = 120/7 min or 17.14 min

• Welcome to MSE. What's new in that answer compared with the answer that was accepted six years ago? Dec 17, 2020 at 14:11
• Well its a different method and as we all know, there are many ways to solve questions in maths...people choose those method which they find easy to understand and practice..and it depends upon speed if we are preparing for competitive exams....i feel that this method is very easy even if the questions are really complex Dec 17, 2020 at 16:48