Question

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?

_________a0 minutes

Answer 1

The power of
The 1st pipe - 1/36
The 2nd pipe - 1/9
The 3rd pipe - 1/12

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

36/8=4.5

The answer is 4.5 minutes.

Answer 2

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.