Pipeline question

Question

I have this multiple choice question from a computer architecture class, a mips processor executes a program at 10 sec, without pipelining and clock rate 100 MHz. When running the program on a processor with 500 MHz clock rate and 5 stages of pipelining which of the following execution times isn't possible. a:2,5 sec, b:3 sec, c:1,5 sec, d:3,3 sec.

My approach to it was to find the cycles of the clock for executing the program on the first processor which would be execution time * clock rate = 1000 * 10^6. From that the number of instructions would be 1000 * 10^6/ first processor's CPI. Since the second processor uses 5 stages of pipelining, I assume it's CPI to be 1 and thus the execution time for it should be 1000 * 10^6/(500 * 10^6 * first processor's CPI) = 2/first processor's CPI and since the CPI of the first processor would have to be 1 or higher the execution time for the second processor would have to be lower than 2 which would mean all choices are correct but c, yet we have been told that the correct answer is c. So c is in reality the only execution time that isn't possible for the second processor but I simply can't figure out why.

Answer 1

From you question, it's not obvious which parts are constant and which are moving, but let's assume that first CPU has the same five execution stages, so each stage takes 2 ns. By pipelining them, we can't improve speed by more than 5x, making 1.5s indeed impossible.

OTOH, improvement may be less than 5x due to structural hazards (as well as memory delays), so all remaining times are possible.