[awagsFare]

The following is the extract from Reliance:

THE END OF THE JOURNEY
f15.7 When the trip ends one must pray the full number of rak`as for each prayer.
A trip ends when one reaches one's hometown. It also ends:

(1) by the mere intention to stay in a place at least 4 full days, not counting the day one arrives or the day one departs;

(2) or by staying that long without the intention, so that after one has stayed 4 full days, not counting the days of arrival and departure, one prays the full number of rak`as,
unless
one is staying in a place in order to fulfill a purpose that one expects to accomplish and intends to leave as soon as one does. As long as this is the case, one may shorten one's prayers for up to 18 days. If longer than this, one prays the full number. This holds for both jihad and other purposes.

-When one reaches one's destination and intends to stay there for a significant amount of time (4 days), one must pray the full number of rak`as,
but
- if not (as when not intending to stay at all, or intending 3 days or less), then one may continue shortening prayers for either 4 days (if one learns that one cannot accomplish one's purpose during them),
or
-18, if one can expect one's purpose to be accomplished at any moment.


So brother basically criterea of 'Duration' for joining prayer is:
-you intent to stay only for 3 days,
-your stay is extended more than 3 days unexpectedly, but you will be leaving as soon as you accomplish your task. But only for 18 days.

There are many other conditions mentioned in the book I shalll copy paste it if you want.