Math 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

Consider V to be the tank volume. Don't worry about how big or small the actual tank is. From the information in the statements, in an hour, all three pipes will pour V/3 + V/4 + V/6 amount of fluid in the tank. That is 9V/12 or 3V/4 . THE WHOLE TANK IS 4V/4 = V in volume.

 

MULTIPLYING our finding for an hour BY 4/3 yields the desired answer. It takes 4/3 hour or 1 hour and 20 minutes for the three pipes operating together to fill the tank of unknown volume V.

Answer 2

Jesse, we solve this problem by looking at how much gets done in one hour. If pipe one fills the tank in 3 hours, then in one hour, 1/3 of the tank is filled, right?

 

So, 1/3 + 1/4 + 1/6 = 1/x

 

What is the LCM of 3, 4, 6 and x? 12x

 

4x/12x + 3x/12x + 2x/12x = 12/12x

 

With the denominators the same, we can actually not pay attention to them.

 

4x + 3x + 2x = 12

9x = 12

x = 12/9 = 1 1/3 = 1 hour and 20 minutes

 

Hope this helps!