Under what circumstances would a user be better off using a time-sharing system, rather than a personal computer or single-user workstation?

When there are some other users, the task is large, and the hardware is fast, timesharing makes sense. The full power of the system can be brought to bear on the user's problem. The problem can be solved faster than on a personal computer. Another case occurs when lots of other users require resources at the similar time.

A personal computer is best when the job is small sufficient to be executed reasonably on it and when performance is sufficient to implement the program to the user's satisfaction.