Puzzle 040: Fill the Reservoir

ナゾ０４０　満タンの貯水池
この貯水池では４台のポンプを使って
湖の水を貯水池に移している。
その４台は１台で運転したときに、それ
ぞれが３日、６日、１０日、１５日で
貯水池を満杯にする能力があるという。
この４台のどれかと同じポンプを、
もう１台追加して、丸１日で貯水池を
ちょうど満杯にしたい。
どのポンプを追加すればよいのだろう？

Google Translate
This reservoir has four water reservoirs are moving into the lake with a single pump. When one of its four operating units are units, each 3, 6, 10, 15 that have the ability to fill the reservoir in the day. This same pump was one of four units, and add another one, just fill the reservoir to round one day. Wonder how do I add a pump?

Notes on Puzzle
You need to fill a reservoir with water. You have four pumps. One pump will fill the reservoir in 3 days; one in 6 days; one in 10 days; one in 15 days. If you want to fill the reservoir in 1 day, you could turn on all the pumps at the same time, but you need one more pump to do it. Is a 3-day pump, 6-day pump, 10-day pump or 15-day pump?