Identical population-splitting events occurred simultaneously on two neighboring islands, Islands B and C, which are each initially home to different populations of rodent. The population-splitting event produced two subpopulations of rodent on each island: B1 and B2, and C1 and C2. We find that populations B1 and B2 cannot successfully interbreed with each other after 50,000 years, and that C1 and C2 can still interbreed after 100,000 years. Why does reproductive isolation arrive at different rates on these two islands

The sub-population of rodents formed in Island B are B1 and B2.
The sub-population of rodents formed in Island C are C1 and C2.
In case of Island B, each of the B1 and B2 sub-populations that got split from each other developed certain mutations that were necessary for them to adapt to the particular diverse environment each of them were exposed to, through the period of 50,000 years. These mutations were so varied that reproductive isolation was generated between them that resulted in each of them to develop into different species.Hence, speciation happens here and B1 and B2 are incapable of inter-breeding.
In case of Island C, each of the C1 and C2 sub-populations that got split might have got exposed to similar environmental change or no environmental change or the environmental change might have been too small to cause drastic change in each of the sub-populations. As a result of this the two sub-populations might have acquired certain mutations to adapt to the environment each of them were exposed to, through a period of 100,000 years. These mutations might not have been too variable or contrasting to cause reproductive isolation between C1 and C2. Hence, no new speciation happens here and C1 and C2 are capable of inter-breeding.