Washer doesn't spin as fast as it should, clothes remain wet.

I have a Kenmore washing machine model # 110.82874100. Serial # C80323994.The spin cycle doesn’t remove all the water from my clothes, and they remain wetter than they have been before. It is not overfilled, it drains correctly. I have looked at the manual and parts list that came with the washing machine. It does not list a drive belt- does it have one? Also, how old is it- 2003 or 1994- not sure how to read number for manufacture year. I know it may be old, but I’m trying to fix instead of throw away. Thank you for all the help.