GRR Controller described an overtake event on final when wind factors were not fully considered during the in trail spacing planning.

Narrative

I was working SAR. NAR had cleared and shipped Aircraft X on the ILS 8R. I then turned Air Carrier Y on a 9 mile final approximately 4.5 miles behind Aircraft X. I shipped Air Carrier Y to the Tower just outside the FAF. Right at that time Tower called down and asked me to break Air Carrier Y out; I told them I didn't have him. Right after that Tower did break Air Carrier Y out to the south. I then turned and commented to the NAR Controller how Air Carrier Y had actually picked up speed on final and how it had gotten pretty close. Shortly after Air Carrier Y came back on frequency he mentioned how they had a 40 KT tailwind on final. I commented that yes; I had noticed how he had actually picked up speed on final. I was told by my Supervisor that they were looking at a possible systems error. I was then shown information from the TARP and saw then what had happened. I would suggest that controllers watch closer the effect that wind is having on aircraft on final and take that into consideration.