Think in terms of rates. The first pipe can fill the tank at the rate of one-eight of a tank per minute and the second pipe can fill the tank at the rate of one-twelfth of a tank per minute. Thus together they can fill the tank at the rate of one-eight plus one-twelfth of a tank per minute.
If both pipes are working how long will it take to fill the tank?
Many students when they see a question like this worry that it looks complicated, but really it is just adding fractions, something you've been able to do for years already.
Let me show you with different figures and then you can try it with your own question.
Pipe one fills 1 tank in 6 minutes, that's 1/6 tanks per minute.
Pipe two fills 1 tank in 9 minutes, so that's 1/9 tanks per minute.
Together, they fill at the rate 1/6 + 1/9. If you make a common denominator and add them, you get 3/18 + 2/18 = 5/18. What does this mean? It means that working together, they can fill 5 tanks in 18 minutes. But since you only want to fill one tank, you have the algebra problem:
5/18 = 1/x
Can you solve this? I get x = 18/5, and that is 3.6 minutes.
Stephen La Rocque.