Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?

### Concept & Proportional Distances When two objects start at the exact same time and travel until they meet, the time they have spent traveling is perfectly equal. For equal times, distance traveled is directly proportional to speed. $$Ratio\ of\ Speeds = Ratio\ of\ Distances$$ ### Step-by-Step Solution 1. **Identify the total distance:** The total distance between the stations is 200 km. 2. **Determine individual distances:** They meet at a distance of 110 km from one station. This means the first train covered 110 km. 3. The second train covered the remaining distance. $$Distance_2 = 200 - 110 = 90 \text{ km}$$ 4. **Calculate the ratio:** Since time is constant, the ratio of their speeds is the same as the ratio of the distances they covered. $$Ratio = \frac{Distance_1}{Distance_2} = \frac{110}{90}$$ $$Ratio = 11 : 9$$ ### Exam Strategy & Shortcut This is an observation-based problem. If total distance is 200, and one piece is 110, the other must be 90. Drop the zeroes: $11:9$. This requires zero calculations on paper. ### Common Pitfall Taking the ratio of the distance met (110) to the total distance (200), getting $11:20$. Always compare the distance of object A strictly to the distance of object B. ### Final Answer Therefore, the correct answer is **11 : 9**.