Arestaurant 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.
b. the manager turns on the restaurant's two neon signs at the same
time. both signs blink as they are turned on. one sign blinks every
9 seconds. the other sign blinks every 15 seconds. in how many
seconds will they blink together again?

a) To find this, we can look at every whole numbered factors of 24.

Those are: 1, 2, 3, 4, 6, 8, 12, and 24.

It can be seen that 1 and 24, 2 and 12, etc. multiply to make 24.

That means our combinations are: 1 person working nonstop, 2 people in 12 hr shifts, 3 people in 8 hr shifts, 4 people in 6 hr shifts, 6 people in 4 hr shifts, 8 people in 3 hr shifts, 12 people in 2 hr shifts, and 24 people in 1 hr shifts.

b) To find this, we have to find the LCM of 9 and 15, which is the smallest number that is the multiple of 9 and 15.

Cake/Tower method:

 |9, 15

3|9, 15

  3, 5

3 * 3 * 5 = 45 seconds