Zuleica's mother Wilma picks her up at the train station when she comes home from school, then Wilma drives Zuleica home. They always return home at 5:00 p.m. One day Zuleica left school early and got to the train station an hour early. She then started walking home. Wilma left home at the usual time to pick Zuleica up, and they met along the route between the train station and their house. Wilma picked Zuleica up and then drove home, arriving at 4:48 p.m. For how many minutes had Zuleica been walking before Wilma picked her up?
Let's name the train station point T, and name the point Zuleica met Wilma on her walk home M. The amount of time saved equals the time it takes Wilma to drive from M to T and back to M again. So driving from M to T must be equal to one half of the total time saved, and also equal to the time Zuleica had been walking. The amount of time saved is 12 minutes (from 4:48 p.m. to 5:00 p.m.). Therefore, Zuleica had been walking for 6 minutes.