basement floor drains

I have 2 basement floor drains that have backed up with water 2 times in the past 2 months. (Home built in 1960 and each time it had rained for a few days) They have never done this before, therefore; the first time it happened I called the county sewer office. They came out and said that everything was running in the city main just fine and the water in the basement was not sewage. (GOOD) Main sewer from house also seems to be working fine. Anyway, after renting a pump and pumping out about 3 inches of water the final inch of water slowly drained away. Then yesterday, again after a few days of rain, I went to the basement and noticed signs of backed up water in the basement that must have drained back down while we were sleeping. We had planned on finishing the basement and really need some help to fix this problem. Again, this has never happened before two months ago and it has rained ALOT worse than the 2 times it's backed up.

 

Where does this floor drain pipe go to? My guess would be since you have no problem with the house drain, it does not connect to the house drain, sound more like a drain for ground water only heading to the outside to a leach line type of drain, in talking about heavy rains, this will cause water tables in the ground to rise, when they rise, at will backup any drains that are below that point. If you know for sure these floor drains are not connected to the house drain, and know for sure these drains serve no other purpose but for being there, plug them off.