Solve the following work problem. one pipe can fill a tank in 36 minutes, a second can fill it in 9 minutes, and a third can fill it in 12 minutes. if the tank is empty, how long will the three pipes, operating together, take to fill it? minutes

Determine the rates for all 3.

First pipe has a rate of 1/36 full per minute
Second pipe has a rate of 1/9 full per minute
Third pipe has a rate of 1/12 full per minute

So if all 3 were operating together, they would have a rate of:

1/36 + 1/9 + 1/12 = 1/36 + 4/36 + 3/36 = 8/36 = 2/9

So the rate for all 3 is: 2/9 full per minute.

So to fill up a tank:

full tank * 1min ÷ (2/9 full) = 4.5 minutes

So it would take 4 and half minutes.