The Winter Garden Hotel has 400 rooms. Every day, the housekeepers clean any room that was occupied the night before. If a guest is checking out of the hotel, the housekeepers give the room a thorough cleaning to get it ready for the next guest. This takes about 30 minutes. If a guest is staying another night, the housekeeper only “refreshes” the room, which takes 15 minutes. Each day, each housekeeper reports for her 6-hour shift then prepares her cart. She pushes the cart to her floor and begins work. She usually has to restock the cart once per day; then she pushes it back to the storeroom at the end of the day and puts the things away. Here is a timetable:

(1) Arrive at work and stock card (10 minutes).

(2) Push cart to floor (10 minutes).

(3) Take morning break (15 minutes).

(4) Stop for lunch (30 minutes).

(5) Restock cart (20 minutes).

(6) Take afternoon break (15 minutes).

(7) Push cart back to laundry and store items (20 minutes).

Last night, the hotel was full (all 400 rooms were occupied).

People are checking out of 200 rooms. Their room will need to be thoroughly cleaned. The other 200 rooms will need to be refreshed.

(a) How many minutes per day of actual room cleaning can each housekeeper do?

(b) How many minutes of room cleaning will the Winter Garden Hotel need today?

(c) How many housekeepers will be needed to clean the hotel today?

(d) If all the guests checked out this morning, how many housekeepers would be needed to clean the 400 rooms?