Question

The Miami Central Hotel has 420 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 25 minutes. If a guest is staying another night, the housekeeper only "refreshes" the room, which takes 20 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 delivers dirty laundry, etc. Here is a timetable:

1) Arrive at work and stock cart (0.10 hrs).

2) Push cart to floor (0.10 hrs).

3) Take morning break (0.33 hrs).

4) Stop for lunch (0.50 hrs).

5) Restock cart (0.30 hrs).

6) Take afternoon break (0.33 hrs).

7) Push cart back to laundry and store items (0.33 hrs).

Last night, the hotel was full (all 420 rooms were occupied). People are checking out of 200 rooms. Their rooms will need to be thoroughly cleaned. The other 200 rooms will need to be refreshed.
How many minutes per day of actual room cleaning can each housekeeper do?

Answer 1

The amount of cleaning time available for each housekeeper is 240.6 minutes. However, to determine how many minutes each housekeeper can clean, we need to know the total number of housekeepers.

Step-by-step explanation:

The question asks how many minutes per day of actual room cleaning can each housekeeper at the Miami Central Hotel do, considering the time they spend on various activities throughout their shift. To determine this, we first calculate the total non-cleaning time by summing the time spent on all listed activities:

• Arrive at work and stock cart (0.10 hrs)
• Push cart to floor (0.10 hrs)
• Take morning break (0.33 hrs)
• Stop for lunch (0.50 hrs)
• Restock cart (0.30 hrs)
• Take afternoon break (0.33 hrs)
• Push cart back to laundry and store items (0.33 hrs)

Adding these up gives a total of 1.99 hours, which is 119.4 minutes of non-cleaning time. A housekeeper's shift is 6 hours (360 minutes). Subtracting the non-cleaning time from the total shift time gives 360 minutes - 119.4 minutes = 240.6 minutes available for cleaning.

Next, since there are 200 rooms that require a thorough 25-minute cleaning and 200 rooms that require a 20-minute refresh, we calculate the total time needed for all rooms:

• Thorough cleaning: 200 rooms × 25 minutes/room = 5000 minutes
• Refresh cleaning: 200 rooms × 20 minutes/room = 4000 minutes
• Total cleaning time required: 5000 minutes + 4000 minutes = 9000 minutes

Without knowing the number of housekeepers, we cannot determine how many minutes each housekeeper can spend cleaning. Therefore, we need additional information about the number of housekeepers to answer the question accurately.