Flag Barges arrive at the Chain of Rocks Lock in Granite City, Illinois at a rate of one every 45 minutes and times between arrivals is exponentially distributed. On average it takes 30 minutes to move a barge through the lock and this time is exponentially distributed. What is the probability that the system has one barge being served and exactly one in the queue? What is the longest average service time for which the average waiting time is less than 50 minutes