Reena leaves office at 6.00 p.m. and catches a 6.30 p.m. local train that arrives in her town at 7.00 p.m. Her father leaves home to pick her up at 7.00 p.m. from the station as she gets off the train. Yesterday, Reena left her office early and took a 6.00 p.m. train and arrived at 6.30 p.m. As her father was not there to pick her up, she started walking towards home. Her father left home at the usual time, saw her daughter walking, turned around, picked her up and drove home, arriving there 10 minutes earlier than the usual. For how long did Reena walk before her father picked her up?

### Concept & Time Savings Principle In problems where a meeting point shifts, resulting in a total time saving, the saved time purely comes from the distance the vehicle *did not have to travel*. By halving the saved time, we can determine the exact time the vehicle intercepted the walking person. ### Step-by-Step Solution 1. **Analyze the Father's Journey:** The father arrived home 10 minutes earlier than usual. This 10-minute saving is strictly because he didn't have to drive the final stretch from the pickup point to the station and back. 2. **Determine One-Way Savings:** Since driving to the station and driving back takes equal time, he saved $10 / 2 = 5$ minutes of driving time *each way*. 3. **Pinpoint the Pickup Time:** Usually, he reaches the station exactly at 7:00 p.m. Because he saved 5 minutes of driving *towards* the station, he must have met Reena 5 minutes before his usual arrival at the station. Pickup Time = 7:00 p.m. - 5 minutes = 6:55 p.m. 4. **Calculate Reena's Walking Time:** Reena arrived at the station early at 6:30 p.m. and immediately started walking. She was picked up at 6:55 p.m. Time spent walking = 6:55 p.m. - 6:30 p.m. = 25 minutes. ### Exam Strategy & Shortcut The core trick is isolating the 10-minute save. 10 mins saved round trip $\rightarrow$ 5 mins saved one way. Usual pickup is 7:00, so new pickup is 6:55. She started walking at 6:30. Difference is 25. You can solve this in your head without a pen once you grasp the logic that the walker's speed or total distance is entirely irrelevant to finding the time! ### Common Pitfall A common pitfall is attempting to find the speed of Reena or her father, or assuming distances. The problem does not provide enough data for absolute speeds or distances, and trying to solve for them will lead to dead ends. Stick purely to the timeline. ### Final Answer Therefore, the correct answer is **25 min**.