Patients use a self$-$serve kiosk to confirm their arrival at an outpatient clinic. They then proceed to the receptionist to update any personal information. After that, a nurse will record the patients' vital signs. A physician will then consult with the patient and prescribe appropriate treatments. The patient will then visit the checkout station to settle payment and schedule the next appointment, if needed. Processing times and other information on the process are presented in the table below. Assume the process started empty. How long would it take to serve $50$ patients?

A$.$ around $6$ hours

B$.$ around $4\mathrm{.}5$ hours

C$.$ around $3\mathrm{.}5$ hours

D$.$ around $7\mathrm{.}5$ hours