At a Hospital Emergency Room, Patients Come in at the Rate

At a hospital emergency room, patients come in at the rate of 20 per hour and on average, are processed at the rate as well. Patients wait in queue till they are called in for registration. After registration, patients are taken to an inner area where they are assigned a bed where they wait till an intern is ready to see them. Once an intern sees them, she either identifies them to be a routine case, prescribes medication and releases them, or she admits them to the hospital for further tests and treatment. On average, it is found that there are 30 patients waiting for registration and another 20 waiting to be seen by an intern.A study has determined that 75% of the patients simply require routine treatment. A new system separates the emergency room into two treatment areas, one for routine care and another for emergency cases. A triage nurse who assigns the patient to one of the two tracks sees a patient after registration. Patients for routine care are seen by an intern who either prescribes medication and releases them or determines that the triage nurse has made a mistake and the patient really needs emergency care. In this case the patient is moved to the emergency track. Patients for emergency care are seen by an intern who either admits them for further treatment or determines that they really are routine cases, prescribes medication and releases them. It is determined that there are, on average, 20 people waiting to be registered, 5 waiting to be seen by the triage nurse, 10 waiting to be seen by an intern in the emergency area, and 10 waiting to be seen by an intern in the routine care area. One average, 75% of the patients are classified by the triage nurse as needing routine care.
(a) On average, how long did patients spend in the emergency room before the triage system (either before being released or admitted)?
(b) On average, how long do patients that are finally admitted to the hospital spend in the emergency room after the introduction of the triage system? Assume that the triage nurse makes no mistake in identifying a patient as needing routine or emergency care.
(c) On average, how long do patients spend in the emergency room after the triage system is introduced (either before being released or admitted)? Assume that the triage nurse makes no mistake in identifying a patient as needing routine or emergency care.