The Passage of Time in Stories and the Rule of Threes
People always say that life's problems (much less the world's problems) can't be solved in half an hour. This refers to after-school programming or family sitcoms wrapping up their issues by the time the end credits roll. What they fail to take into consideration is the fact that these stories do not play out in real time. Their time allotment may be thirty minutes (minus about five to eight for commercials), but they aren't consecutive minutes. Realistically, how long these issues take to resolve themselves is clearly up to the writer as well as any other restrictions or demands on the storytelling process. That often involves the rule of three, but not always.
On television, characters' problems are often milked for as long as they can provide fodder, pathos, and ratings before their ultimate resolution. This can be achieved in several different ways as far as television scripts are involved; depending on how they might be solved, this does not always have an ending that is satisfactory to the audience. When television was simpler, half an hour was enough to tell a simple tale, especially when teaching the audience an Aesop (fable or PSA). In the case of the written word, time can drag on as long or as short as the author requires to tell a complete story. For example, each book in the Harry Potter series explores a year in Harry's life. No one would accuse J.K. Rowling of solving Harry's problems in the time it takes the average reader to complete the book (anywhere from one weekend to one week) or the running time of any of the movies. The cameras don't stay on the characters 24/7, nor does the focus of the story as presented by a narrator. Why should television be looked at any differently in these instances?
While I cannot pinpoint the average amount of time that would be "appropriate" for solving life's problems in a more "realistic" manner, the rule of three comes up often enough. For instance, I have noticed that three days is a common time-frame for guests to stay at a protagonist's home while they work on their problems. This passage of time can either be marked officially by caption panels or left to the imagination of the audience. In Fruits Basket, it is stated outright on three separate occasions that characters had been staying over for three days just before their problems are ultimately solved in some way. Prior to this, the Japanese tradition of visiting a relative's home for the first three days of January in celebration of the new year had been mentioned but not explored. Additionally, not all three days had been marked in full - the audience just had to take the narration's word for it. This was also the case in Disney's Beauty and the Beast, in which (unbeknownst to me until a bygone Internet reviewer pointed it out) Belle spends a total of three days in Beast's castle. For future reference, montages can throw off an audience's sense of time, especially when costume changes do not happen at regular intervals either inside or outside of it.
In conclusion, there are no written rules dictating how long fictional problem-solving should take, only customary routines and unfounded judgments debating their realism and practicality. There should be no limits to creativity and therefore no box defining its parameters, time included. While there is something to be said for the skill of timing out events, they will unfold in a way the writer finds suitable, and the audience will have to decide for itself whether or not to suspend their disbelief or expand their understanding of the matters at hand.