Q$1$: In Data Structures class, you developed a program that processes a large dataset. Let's analyze the performance of that program on two different systems.On System X$,$ the program runs in $15$ seconds, and the system has a clock speed of $3$ GHz$.$ Now, we want to design a new system, System Y$,$ that will execute the same program in $9$ seconds.The designer of System Y has discovered that achieving a higher clock speed is feasible, but this improvement comes with a cost: System Y will require $1\mathrm{.}5$ times as many clock cycles as System X to complete the program.What clock rate should we recommend to the designer for System Y$?$By how much System Y faster than System X$?*$Show your steps on how you get the answers!