Patients arrive to Mount Sinai Emergency Room at an average rate of 40 per hour. There are two types of patients: those who enter the system and eventually see a doctor, and those who balk immediately without entering the system (if they perceive that the wait will be too long). Patients who enter the system first delay in a wait area before seeing a doctor. The wait area has 80 chairs. The average number of patients in the wait area is 50 (this does not include the balkers who do not enter the wait area). All the patients who have entered the wait area will eventually see a doctor, and the average delay for these patients in the wait area is 2 hours. There are always 15 doctors on staff at all times, and we can consider that they are 80% utilized on the average.

a) What is the average rate at which potential patients balk?

b) What is the average time spent seeing a doctor?