Suppose that two shuttle buses operate $($without coordination$)$ between the campus and downtown. One bus can carry $20$ people and has a round trip time of $8$ min $($including boarding and unloading passengers$),$ the other can carry $25$ people bus has a round trip time of $10$ min. There is always a queue of people waiting at the downtown bus stop, but passengers come to the campus bus stop at steady rate of $2/$min$.$ If neither bus is idle at ay time, determine:

a$)$ The flow of people from downtown to campus.

b$)$ The flow of people from campus to downtown.

c$)$ The average bus occupancy from campus to downtown