Gabriela is the CEO of an innovative architectural firm that builds tall buildings using wood (such firms exist, by the way). She typically leaves her office in time to catch the 5:00 commuter train that takes her to the town of Newburyport. Nazir, her chauffeur, arrives at the station just at 5:00 and drives her to her comfortable zero-emission house out in the country.
One sunny day, Gabriela was able to leave her office early, and she caught the 4:00 train. When it got to her station early, and since it was a nice day, she decided to walk toward home, knowing that she would encounter Nazir and her car along the way. Indeed, this happened: she saw Nazir driving toward her, flagged him down, and rode the rest of the way home. She arrived 40 minutes earlier than usual.
Question: for how many minutes did she walk before Nazir picked her up?
Solution
To solve this problem, switch gears from thinking about Gabriela to thinking about Nazir. He, too, arrived at her house 40 minutes early. This means that he didn't drive the last 20 minutes of the trip to the train station, nor did he drive the first 20 minutes of the trip back. Thus he picked up Gabriela at 4:40, 20 minutes early. And since she started walking at 4:00, she walked for 40 minutes.
A dandy problem, that can be solved without paper and pencil.