> ... if a program needs 20 hours to complete using a single thread, but a one-hour portion of the program cannot be parallelized ... then regardless of how man

> ... if a program needs 20 hours to complete using a single thread, but a one-hour portion of the program cannot be parallelized ... then regardless of how many threads are devoted to a parallelized execution of this program, the minimum execution time cannot be less than one hour. It really does seem obvious. You can either do the sync part before or after the parallelized part. Since you cannot have infinite horizontal compute, the parallelized part will take some ε > 0 of time to finish, and the total execution time will be 1 + ε.