Suppose you cycle 10.0 km to the east and 15.0 km north to get to a shopping mall from home. After doing your shopping you cycle 5.0 km to the west and 14.1 km south-west to meet your friend for a drink.
If you have a homing pigeon (a trained pigeon that can find its way home directly), what is the direction the the pigeon should fly and how far must it travel to get home in the shortest time?