The Hadith of the Messenger of Allah (saw):
لَا يَحِلُّ لِامْرَأَةٍ تُؤْمِنُ بِاللَّهِ وَالْيَوْمِ الْآخِرِ تُسَافِرُ مَسِيرَةَ يَوْمٍ وَلَيْلَةٍ إِلَّا مَعَ ذِي مَحْرَمٍ عَلَيْهَا
"It is not permissible for a woman who believes in Allah and the Last Day to travel for a duration of a day and a night except with a mahram over her." (Narrated by Muslim on the authority of Abu Hurairah, may Allah be pleased with him):
1 - It is prohibited for her to travel alone without a mahram for the mentioned duration, i.e., a full day (24 hours), night and day.
2 - The text indicates time and not distance. If she travels a thousand kilometers by plane without a mahram but goes and returns without staying for that duration, it is permissible for her. However, if she walks twenty kilometers and it requires more than a day and a night, it is prohibited for her without a mahram.
3 - The texts regarding shortening the prayer (qasr) and the permissibility of breaking the fast (iftar) involve distance (four burud), which is estimated at approximately 89 kilometers. The distance is what is considered for shortening; whoever travels this distance by plane, ship, or on foot is permitted to shorten, regardless of the travel time.
4 - Therefore, the criterion for a woman traveling without a mahram is time—a day and a night—regardless of the distance. If the woman does not stay for this amount of time, but rather travels and returns before it, then her going without a mahram is permissible. As for shortening the prayer and breaking the fast, the criterion is distance, regardless of whether the time is short or long.
5 - As for her safety, this is another matter. If she is not safe except with a mahram, she should not travel even if the duration is half a day, as personal safety is a separate issue.
6 - A mahram is a man from the woman’s unmarriageable relatives. While some jurists allow traveling with "trustworthy women," we prefer that she travels with a male mahram for the required distance.
7 - A person traveling for a short course, for a period of three months for example, is treated as a traveler if they do not take the country where the course is held as a place of residence, but rather only to attend the course and return to their original country. In this case, their ruling is that of a traveler. However, if they take the country where the course is held as a residence, then in this case their travel is interrupted, and they take the ruling of a resident.