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P$4$: $(20$ pts$)$ River City Hospital has a busy diagnostic imaging department that operates several MRI scanners. Each MRI scan takes an average of $30$ minutes,

including the time to prepare the patient and perform the scan. The hospital schedules patients for MRI scans at regular intervals, sending a patient to the MRI

room every $15$ minutes.

A$.$ How many MRI machines are in use at any given time at River City Hospital?

B$.$ The hospital's director of imaging proposes reducing the time between patients by scheduling scans every $5$ minutes, arguing that this will decrease the

average time a patient spends in the MRI room to $20$ minutes. Is the director's claim correct? If not, what will the actual average time spent in the MRI

room be$,$ given this new scheduling interval?