Question

One pipe fills a tank in 1 hour while another pipe can fill the same tank in 2 hours. How long will it take to fill the tank if both pipes are used?

Answer 1

The filling rate of the first tank is this: $\frac{1 tank}{1 hour}$
The filling rate of the second tank is this: $\frac{1 tank}{2 hours}$
Add them to get the combined rate: 
$\frac{1 tank}{1 hour} + \frac{1 tank}{2 hours}$
Make a common denominator by multiplying the first fraction by 2/2:
$\frac{2 tanks}{2 hours} + \frac{1 tank}{2 hours}$
Adding them together, we get:
$\frac{3 tanks}{2 hours}$

So, now we know that the combined rate is 3 tanks per 2 hours... but we need to know how long it will take to fill only one tank. So, we need to find the unit value, which we do by doing this: 
$\frac{3}{2} = \frac{1}{x}$
Then we can cross-multiply:
$3x = 2$
And divide both sides by 3 to get our final answer:
$x = \frac{2}{3}$

So, it takes 2/3 of an hour, or 40 minutes.

Hope I helped, let me know if you have any questions :)