You drive $12$ miles on your way to college campus and it takes' you $25$ minutes. Before you park your car, you realize that you forgot your wallet. You immediately return home via the same route of $12$ miles. This time around it takes you $30$ minutes to arrive home.$$

$$(a$)$ Which way, going to campus or returning home was your average speed greater?

$($b$)$ Considering the entire trip, i$.$e$.,$ from home to campus then back home, what is the average speed?$$

$($c$)$ Considering the entire trip, i$.$e$.,$ from home to campus then back home, what is the total displacement?$$

$($d$)$ Considering the entire trip, i$.$e$.,$ from home to campus then back home, what is the average velocity?