Consider a walkup service center that is modeled by an M$/$M$/1$ queuing system $($Poisson arrivals and exponential service times$),$ where the average inter$-$arrival time is $50$ seconds. Customer service times are currently on the increase, and management will add a second server once average waiting time in the queue reaches $12$ minutes. What is the average service time $($in seconds$)$ that will result in an average waiting time in the queue of $12$ minutes for this M$/$M$/1$ system, thereby creating the need for a second server?