Assuming a serial runtime of 64s a parallel runtime of 24s o

Solution

Serial run-time = 64s implies a single core requires 64s to compute that task.

Using 4 such cores parallely, the task should actually require 64s/4 = 16s. As it requires 24s, the fixed overhead is 24s - 16s = 8s.

If 8 such cores are used, then each core will require 64s/8 = 8s. If they run parallely just 8s would be sufficient, but the above overhead should be required here also. As it is given that the overhead is fixed with 8s, the expected speedup with eight cores would be 8s + 8s = 16s. (If the overhead varies based on the number of cores used, then the speedup may vary). With the fixed overhead, it can be taken as 16s easily and the speedup ratio would be 64s/16s = 4. Hence the speedup ratio is 4 and 8 cores parallel processing require 16s.