We fast at various times during the year because of the catastrophes and tribulations associated with those dates. However, contrary to popular belief, the purpose of these fasts is to awaken us and stir our hearts toward teshouba by recalling our own misdeeds as well as those of our ancestors. By remembering these misdeeds, which we continue to repeat and which bring on similar calamities, we are motivated to return to the proper path, as we read in the Torah: But if they will confess their sins and the sins of their fathers etc (Vayikra 26:40).
Each individual should use these days to engage in self-examination and to repent, for the essential purpose of a fast day is to motivate one to repent, as the verse (Yonah 3:10) states in regard to the people of Nineveh: And Hashem saw their actions. There are various ways to interpret the verse, but our rabbis in the Gemara explain that the verse does not state that God saw their sackcloth and fasting, but their actions, for the purpose of fasting is to bring one to repent. (Ta'anit 22a)
Therefore, even those who spend the fast day working, still need to emphasize this essential element of the day. One needs to refocus their lives on Torah and ideals of the Torah. Nonetheless, repentance alone, without fasting, is insufficient, assuming one is healthy and able to fast, for it is an ordinance established by the Prophets, and all Yisrael has accepted these fast days throughout the generations.