A hospital has 30 labor rooms, 15 combination labor and delivery rooms, 3 delivery rooms, and 1 special delivery room reserved for complicated births. All rooms operate around the clock. Time spent in labor rooms varies from hours to days, with an average of about a day. The average uncomplicated delivery requires about one hour in a delivery room.

During a three day period, 109 healthy babies were born. 60 babies were born in separate labor and delivery rooms, 45 were born in combined labor and delivery rooms, and only 4 babies required a labor room and the complicated delivery room. Which had the greatest utilization rate?

To determine which room had the greatest utilization rate, we need to compare the number of babies born in each type of room to the total number of available hours in that room.

Let's calculate the utilization rate for each room type:

1. Labor Rooms:
- There are a total of 30 labor rooms.
- The average time spent in a labor room is about a day, which is equivalent to 24 hours.
- The total available hours in labor rooms over a three day period is 30 labor rooms * 24 hours/day * 3 days = 2,160 hours.
- From the given information, we know that 4 babies required a labor room and the complicated delivery room.
- Therefore, the utilization rate for labor rooms is 4 babies / 2,160 hours = 0.00185 babies/hour.

2. Combination Labor and Delivery Rooms:
- There are 15 combination labor and delivery rooms.
- As mentioned, the average time spent in a labor room is about a day, which is equivalent to 24 hours.
- The total available hours in combination labor and delivery rooms over a three day period is 15 rooms * 24 hours/day * 3 days = 1,080 hours.
- From the given information, we know that 45 babies were born in combined labor and delivery rooms.
- Therefore, the utilization rate for combination labor and delivery rooms is 45 babies / 1,080 hours = 0.0417 babies/hour.

3. Delivery Rooms:
- There are 3 delivery rooms.
- The average time spent in a delivery room for an uncomplicated birth is about 1 hour.
- The total available hours in delivery rooms over a three day period is 3 rooms * 1 hour/complicated birth * 3 days = 9 hours.
- From the given information, we know that 60 babies were born in separate labor and delivery rooms.
- Therefore, the utilization rate for delivery rooms is 60 babies / 9 hours = 6.67 babies/hour.

4. Special Delivery Room:
- There is 1 special delivery room reserved for complicated births.
- The average time spent in the special delivery room is unknown in the given information.
- However, since only 4 babies required the special delivery room, the utilization rate cannot be calculated as we don't have the total available hours.

Comparing the utilization rates calculated above, we can see that the delivery rooms had the greatest utilization rate with 6.67 babies/hour.