There is a water-cask with three different water-taps. With the smallest tap, the water-cask can be filled in 20 minutes. With the middle tap, the water-cask can be filled in 12 minutes. With the largest tap, the water-cask can be filled in 5 minutes.
How long does it take to fill the water-cask with the three taps together?
The smallest tap fills 1/20 water-cask in 1 minute. The middle tap fills 1/12 water-cask in 1 minute. The largest tap fills 1/5 water-cask in 1 minute.
Together they fill 1/20 + 1/12 + 1/5 = 1/3 water-cask in 1 minute. Therefore, the whole water-cask is filled in 3 minutes.