This is a beautiful puzzle for children from the book Mathematical Circle Diaries, Year 1 (Session 22, last puzzle).
Two mountain villages, Belleview and Hillview, are connected by a road. Not a single stretch of this road is flat: the road always goes either uphill or downhill. A round trip on a bus between these two villages takes 6 hours. The speed of the bus on any uphill section of the road is 30 miles per hour, and on any downhill section it’s 60 miles per hour. Find the distance between the these villages.
As always, please send your answers directly to me at email@example.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.