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To answer the question, we should know first where these members of the family came from and what day they each flew from their respective origins. If the maximum number of days is 15 days to get there, then in less than 2 weeks and 1 day all members of the family should arrive on the same place. But whether their arrivals were on the same day or not, that can never be answered unless we know where and when they depart.

Members of the family that depart from same place will surely arrive on the same day in less than 2 weeks and 1 day.

Members that flew from different areas but with the "same or almost the same length"of flying time will also arrive on the same day (depending on the time that they depart). Otherwise, some would arrive early and others would arrive few hours after the start of the next day (or midnight). But surely all will arrive still in less than 2 weeks and 1 day.

And finally, if all flew from different places with a big gap of distance to their final destination then they can surely not arrive on the same day.

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Q: If there are twenty weeks and a family wants to arrive on the same day and the highest amount of days it takes to get there is fifteen days how many weeks could they arrive on the same day?
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