a resturant is open 24 hours a day. T he manager wants to divide the day into work shifts of equal length. The shifts should not overlap. All shift durattions should be a whole number of hours. Describe the different ways this can be done.
Factors of 24
4 * 6
3 * 8
2 * 12
the factors of 24 are
1,2,3,4,6,8,12,24
Now you take it.
To find the different ways the manager can divide the day into work shifts of equal length, we can consider the factors of 24 since the restaurant is open 24 hours a day. Factors are numbers that divide a given number evenly without leaving a remainder. In this case, we need to find the factors of 24 and identify which of those factors represent a whole number of hours for a work shift.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24. Let's examine each of these factors to see if they can represent a whole number of hours for a work shift:
1 hour shift: This would result in 24 shifts, but it wouldn't be practical considering the frequency of shift changes throughout the day.
2 hour shift: This would result in 12 shifts, where each shift covers a span of 2 hours.
3 hour shift: This would result in 8 shifts, where each shift covers a span of 3 hours.
4 hour shift: This would result in 6 shifts, where each shift covers a span of 4 hours.
6 hour shift: This would result in 4 shifts, where each shift covers a span of 6 hours.
8 hour shift: This would result in 3 shifts, where each shift covers a span of 8 hours.
12 hour shift: This would result in 2 shifts, where each shift covers a span of 12 hours.
24 hour shift: This would result in a single shift covering the entire day, which wouldn't satisfy the requirement of multiple, non-overlapping shifts.
Given these options, the different ways the manager can divide the day into work shifts of equal length are as follows:
- 2-hour shifts (12 shifts)
- 3-hour shifts (8 shifts)
- 4-hour shifts (6 shifts)
- 6-hour shifts (4 shifts)
- 8-hour shifts (3 shifts)
- 12-hour shifts (2 shifts)
The manager can choose any of these options depending on the operational requirements and the availability of employees.