To determine the number of shifts needed each week for the nurses working at the hospital, we start by understanding a few key points:
1. Shift Duration: Each nurse works for 8 hours per shift.
2. Daily Coverage Requirement: The hospital requires 24 hours of coverage each day.
To find out how many 8-hour shifts are required to cover a full 24-hour day, we divide the total number of hours in a day by the duration of each shift:
[tex]\[ \text{Shifts per day} = \frac{24 \text{ hours/day}}{8 \text{ hours/shift}} \][/tex]
Using the figures provided:
[tex]\[ \text{Shifts per day} = \frac{24}{8} = 3 \][/tex]
Thus, 3 shifts are needed to cover each day of the week.
Now, we need to determine how many shifts are required for the entire week. Since a week has 7 days, we multiply the number of shifts per day by the number of days in a week:
[tex]\[ \text{Shifts per week} = 3 \text{ shifts/day} \times 7 \text{ days/week} \][/tex]
Calculating this, we get:
[tex]\[ \text{Shifts per week} = 3 \times 7 = 21 \][/tex]
Therefore, the total number of shifts that need to be filled each week is [tex]\( \boxed{21} \)[/tex].
