Question

A restaurant is open 24 hours a day. The manager wants to divide the day into work shifts of equal length. The shifts should not overlap. All shift durations should be a whole number of hours. Describe the different ways this can be done.

Answer 1

Some possible answers are:

Three 8-hour shifts; four 6-hour shifts; six 4-hour shifts.

Explanation:

We want factors of 24 for the shifts, since the shifts cannot overlap. The factors of 24 include:

1, 2, 3, 4, 6, 8, 12, 24

A 1-hour shift does not make much sense; most employers will also not use a 2-hour or 3-hour shift. Restaurants typically do not use 12-hour shifts either, and employers do not use 24-hour shifts either. This leaves 4, 6, and 8.

If we use 4-hour shifts, we would have 24/4 = 6 of these shifts.

If we use 6-hour shifts, we would have 24/6 = 4 of these shifts.

If we use 8-hour shifts, we would have 24/8 = 3 of these shifts.

Answer 2

With two employee shifts, each will work 12 hours  (2 x 12)
With three employee shifts, each will work 8 hours (3 x 8)
With four employee shifts, each will work 6 hours   (4 x 6)
With six employee shifts, each will work 4 hours   ( 6 x 4)
With twelve employees shifts, each will work 2 hours   ( 12 x 2)