Word Problem (intermediate Algebra)

Question

One pipe can fill a tank in 3 h, a second pipe can fill the tank in 4 h, and a third pipe can fill the tank in 6 h. How long would it take to fill the tank with all three pipes operating?

Answer 1

Hi Alison.

 

Let's call the volume of the tank V. We'll assume it's measured in liters (though it doesn't really matter).

 

Pipe 1 fills at a rate of V/3 liters/hr.

Pipe 2 fills at a rate of V/4 liters/hr.

Pipe 3 fills at a rate of V/6 liters/hr.

 

We want to know how much time it takes for all three combined to fill the tank (that is, reach a volume of V liters). We'll call that time t.

 

If all three pipes are running at the same time, that means that your flow rate is:

 

(V/3 + V/4 + V/6) liters/hr

 

Now, since

 

Flow Rate * Time = Volume

 

That means:

 

(V/3 + V/4 + V/6)*t = V

 

(4V/12 + 3V/12 + 2V/12)*t = V

 

(9V/12)*t = V

 

t = 12V/9V

 

t = 12/9

 

t = 4/3 hours

 

or

 

t = 1 hour 20 minutes

 

Hope this helps.