System $1$ An average of $40$ customers arrive each hour; interarrival times are exponential. Customers must complete three types of service before leaving the system. The first server takes an average of $30$ seconds $($exponentially distributed$)$ to perform type $1$ service. After waiting in line, each customer obtains type $2$ service $($exponentially distributed with a mean of $1$ minute$)$ from a single server. After completing type $2$ service, a customer will go to obtain type $3$ service $($exponentially distributed with a mean of $30$ secnds$)$ from a single server. After completing type $3$ service, a customer leaves the system. System $2$ The arrival process for system $2$ is identical to the interarrival process for system $1.$ In system $2,$ a customer must complete only one type of service. Service time averages $2\mathrm{.}0$ minutes and is exponentially distributed. Three servers are available. In which system does a typical customer spend less time? Please justify your answer with your step by step analysis results.