SOLUTION: 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 i

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Question 1119737: 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 by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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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?
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Before answering question a), I would like to re-formulate it to make it more clear.

So, my reformulation is THIS 

    a.  Will the 30-th day from today be Julie's working day or the day off ?

Now I am ready to answer. 

    Notice that Julie's schedule is PERIODIC, and the period is exactly 2 weeks = 14 days.


    Thus the first day is the first day of the period;

    then the 15-th day is the first day of the second period;

    then 29-th day is the first day of the third period.


    Hence, 30-th day is the second day of the period, and it is her working day, according to the description.


The method to solve this and similar problems is to identify the period and then move forward period after period.

Or, in other words, to identify the period and throw away the integer number of periods.

You can answer the next question b) using the same method and same idea.

Please try to do it on your own.