Question 4: A hospital emergency room (ER) is currently organized so that all patients go through an initial registration and triage by a nurse.

Question 4:

A hospital emergency room (ER) is currently organized so that all patients go through an initial registration and triage by a nurse. Once the triage and registration is done, at his or her turn, each patient is seen by a doctor and then exits the process, with a prescription (Type-I), or with referral to a specialist (Type-II), or with admission to a hospital (Type-III). Currently, 30 patients per hour arrive at the ER; 60%, 20%, and 20% of whom are Type-I, Type-II, and Type-III patients, respectively. On average, 6 people are waiting to go through triage and registration and 24 are registered and waiting to see a doctor. The triage and registration process takes, on average, 6 minutes per patient. The doctor, on average, spends 10, 20, and 30 minutes, for each Type-I, Type-II, and Type-III patient, respectively.

b) On average, for how many minutes does a patient stay at the ER? (Show all your work!)

c) Determine the bottleneck operation, and explain why it is the bottleneck. d) Propose two performance-improvement suggestions for the ER process above. 

Hi there, I am unsure how to solve b) in this question! I know it requires using Little's Law (I=RxT), but I can't figure it out.