The speeds of John and Max are 30 km/h and 40 km/h. Initially Max is at a place L and John is at a place M. The distance between L and M is 650 km. John started his journey 3 hours earlier than Max to meet each other. If they meet each other at a place P somewhere between L and M, then the distance between P and M is:

### Concept & Relative Speed When two objects move towards each other, their relative speed is the sum of their individual speeds. Before applying relative speed, we must first determine the remaining distance between them at the exact moment both are moving simultaneously. $$Relative Speed = S_1 + S_2$$ ### Step-by-Step Solution 1. John's speed is 30 km/h, and Max's speed is 40 km/h. Initial distance is 650 km. 2. John starts from M, 3 hours earlier than Max. 3. Distance covered by John in these 3 hours: $$Distance = 30 \times 3 = 90 \text{ km}$$ 4. Remaining distance between John and Max when Max starts moving: $$Remaining Distance = 650 - 90 = 560 \text{ km}$$ 5. Now both are moving towards each other. Their relative speed: $$Relative Speed = 30 + 40 = 70 \text{ km/h}$$ 6. Time taken for them to meet after Max starts: $$Time = \frac{560}{70} = 8 \text{ hours}$$ 7. The meeting point P's distance from M is exactly the total distance John traveled. 8. Total time John traveled = 3 hours (alone) + 8 hours (with Max moving) = 11 hours. 9. Distance from M to P = John's total distance: $$Distance = 30 \times 11 = 330 \text{ km}$$ ### Exam Strategy & Shortcut Separate the head start from the simultaneous movement. Calculate the head start distance (90 km). The remaining 560 km is closed at a combined speed of 70 km/h, which takes 8 hours. The question asks for distance from M (John's start). John travelled for $3 + 8 = 11$ hours at 30 km/h. $11 \times 30 = 330$ km. ### Common Pitfall Calculating the distance from L (Max's start point) instead of M. Max travels for 8 hours at 40 km/h = 320 km. Selecting 320 km would be incorrect as the prompt asks for distance between P and M. ### Final Answer Therefore, the correct answer is **330 km**.