Problem $3-18($Algo$)$

You are responsible for setting up the front desk for Redi$-$Help Emergency Care systems. In conversation with the owners of this new facility, Hope Hospital Systems, you have found that the waiting room will accommodate $50$ patients. However, management wants no more than $86\%$ utilization for the waiting room. At peak times $($e$.$g$.,$ for flu season testing or COVID$-19$ testing$),$ it is anticipated that $68$ patients would be arriving per hour.

a$.$What is the waiting time in minutes? $($Hint: Focus on wait time.$)$

Note: Do not round intermediate calculations. Round the final answer to the nearest whole number.