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?

The filling rate of the first tank is this: 
The filling rate of the second tank is this: 
Add them to get the combined rate: 

Make a common denominator by multiplying the first fraction by 2/2:

Adding them together, we get:


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: 

Then we can cross-multiply:

And divide both sides by 3 to get our final


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

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