Unit rate is defined as the amount of work done per unit time. In this case, the "work" refers to the amount of parts made. Unit time is then measured in hours. Since the given problem states the total number of parts manufactured and the total time of manufacturing, we simply have to divide the number of parts by the manufacturing time to obtain the unit rate. This is done as follows:
Unit rate = total number of parts manufactured / total manufacturing time
Unit rate = 1630 parts / 6 hours
Unit rate = 271.667 parts/h
Therefore the unit rate is approximately 272 parts/h.