the total distance that martina travels that day is
(distance from home to mom's office) plus (distance from mom's office to school)
plus (distance from school to library) plus (distance from library to friend's house)
plus (distance from friend's house to martina's house).
(we don't know what any of these distance actually is.)
I have watched "Sherlock Holmes". It is a story chain of various deeds of a British detective. He uses his senses with full confidence in order to solve various puzzles. He uses detailed observation of any incident or any character.
He collects information from his logic and creates his own story which seems to be fit in given circumstances. He uses deductive reasoning in order to reach to a conclusion. There are various scenes in this whole series where he can tell the whole schedule of a person just simply observing his/her coat.
I remember a scene in which a person comes to him. He just looks at him for few seconds. Sherlock notices tea stain on his coat. In the very next minute, Sherlock asks him, how bad was his morning? The person gets confused and surprised also.
He asks the reason behind Sherlock's question. Sherlock tells him a story based on his deductive reasoning. He tells him about the noticing of tea stain. He also explains size and configuration of that stain. He also elaborates that such dimensions can be obtained only in a fast moving object when someone has fight at the same time.
He also tells him some other details. All these were based on his extreme senses and his detailed perceptions about the circumstances. Sherlock considers his perceptions as real and tests them according to his knowledge and logical reasoning. He mixes all these things with his deductive reasoning which provides him a meaningful story.