b$)$ Assume the pediatrician$$s office is open $8$:$00$ a$.$m$.$ to noon. Arrivals and departures to a pediatrician$$s office are collected and reported below. Given these, how many patients on average are in the office?

Patient Arrival Departure

$18$:$008$:$30$

$28$:$159$:$30$

$310$:$0010$:$30$

$410$:$1511$:$15$

$510$:$4512$:$00$