Question

Julie, a police officer, has the following work pattern. She works 3 days, has 4 days off, then works 4 days, then has 3 days off, and then the pattern repeats. Assume that today is the first day of the work pattern. Answer the following questions showing the computations that support your answer. a. Will Julie be working 30 days from today? b. Julie's niece is getting married 45 days from today. Will Julie have the day off?

Answer 1

a) Yes, she would have day off, 30 days from today Julie will be off work and have a day free as that day would be day 30 and day one stays inclusive, the day after also proves day 31 is a day off as it shows week 4 last day off being day 31 and day 30 is also day off week 4.

As 7 x 4 = 28 and she is back at work day 29 and day 30 she is free and not at work, her 5th pattern for that month and it goes back to 3 days week five.

b) Yes, Julie would have day off on day 45.

As 7,14,21,28,35,42,49 are 6 weeks but dates show and prove below. As 45 is the first day off in week 7 as we prove 4 days off in that week.

Explanation:

As days work like this

Wk 1 3 days on 4 days off = day 1 - 7 = 7 days

Wk 2 4 days on 3 days off = 8 - 15 = 7 days

Wk 3 3 days on 4 days = 16 - 23 = 7 days

Wk 4 4 days on 3 days off = 24 - 31 = 7 days

Wk 5 3 days on 4 days off = day 32 -39 = 7 days

Wk 6 4 days on 3 days off = day 40 - 44 at work and 45-47 is not at work = 7 days Which means 45 she is off work.

Wk 7 3 days on 4 days off = day 48, 49, 50 then day 51-54 she is scheduled to not work.

If we take day 51 day off and minus 4 days off

51-4 = 47 and she had 3 days off from 45-47 to match this which would include day 45.

Answer 2

See below.

Explanation:

For each day number, Y means working, and N means off

Day

1 Y

2 Y

3 Y

4 N

5 N

6 N

7 N

8 Y

9 Y

10 Y

11 Y

12 N

13 N

14 N

15 Y

16 Y

17 Y

18 N

19 N

20 N

21 N

22 Y

23 Y

24 Y

25 Y

26 N

27 N

28 N

29 Y

30 Y

31 Y

32 N

33 N

34 N

35 N

36 Y

37 Y

38 Y

39 Y

40 N

41 N

42 N

43 Y

44 Y

45 Y

46 N

a. Today is day 1. 30 days from today is day 31.

She works on day 31, so she does work 30 days from today.

b. 45 days from today is day 46. She is off on day 46, so she will be off 45 days from today.