John Smith needs to decide where to have his car handwashed. He has narrowed the choice down to two local car washes $$ Deluxe Handwash Center $($DHC$)$ and Compact Car Spa $($CCS$).$

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During busy periods, a new car arrives at DHC every $15$ minutes $($with a standard deviation of $15$ minutes$).$ At CCS$,$ a car arrives every hour $($with a standard deviation of $1$ hour$).$ DHC has a team of $4$ handwash specialists, while CCS has $1$ specialist. Typical handwashing service time at either place lasts $30$ minutes $($with a standard deviation of $30$ minutes$).$

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If John drives into DHC during a busy period, how long must he wait before his car can be handwashed? $($Note: Only include the waiting time, not the service time.$)$ Round your answer to two decimal places.

minutes

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If John goes to CCS$,$ how long must he wait before his car handwashing starts? Round your answer to two decimal places.

minutes

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Assume it takes John $10$ minutes to drive from work to DHC and $10$ minutes to drive back. How long will he need to be away from work to have his car handwashed at DHC$?$ Round your answer to two decimal places.

minutes

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DHC will buy out CCS$.$ Following the merger, DHC will close CCS$$s operations and serve all customers, including those from CCS$,$ at the DHC location only. Assuming that the previous traffic of CCS customers now flows to DHC$,$ what is the new interarrival time at DHC$?$ Round your answer to two decimal places.

minutes

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DHC retains the specialist of CCS and now has a team of $5$ specialists. Is the new waiting time at DHC less than or greater than the waiting time before the merger? $($Note: Assume that the coefficient of variation of customer interarrival times is $1).$ Round your answer to two decimal places.

minutes