Company U$-$Be$-$See currently has three counters, each staffed by a single employee, and a single first$-$come$-$first$-$serve queue for all customers to join. You think that the current system is wrong. You would like to redesign the queues so that there is a dedicated queue and a dedicated server for each customer type $($type $1,$ type $2,$ and type $3).$ No customers cross between servers.

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Type $1$ clients arrive at a rate of $30$ per hour.

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Type $2$ clients arrive at a rate of $15$ per hour.

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Type $3$ clients arrive at a rate of $6$ per hour.

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Each of the three serving employees takes an average of $3$ minutes to complete a transaction.

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Assume inter$-$arrival and service times follow an exponential distribution.

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Find the total time in the existing system $($waiting and service time$).$