Two trains start toward each other from cities 600 km apart, one at 90 km/h and the other at 110 km/h. How far from the first train’s start point do they meet?
["Title: Solve the Classic Train Meeting Distance Problem: Where Two Trains Overtake Each Other", "When two trains travel directly toward each other from opposite cities hundreds of kilometers apart, many wonder: At what distance from the starting point of the faster train do they meet? This classic physics and relative motion problem is a perfect example of applying time and distance relationships. Let’s solve it step by step.", "### The Scenario", "Two trains set off from cities 600 km apart, heading straight toward each other:", "- Train A (starting point 1) travels at 90 km/h\n- Train B (starting point 2) travels at 110 km/h", "The trains move toward a common meeting point between the two cities, which are 600 km apart.", "---", "### Step 1: Calculate the combined speed", "Since the trains are moving toward each other, their relative speed is the sum of their speeds:", "[\n\ ext{Relative speed} = 90,\ ext{km/h} + 110,\ ext{km/h} = 200,\ ext{km/h}\n]", "---", "### Step 2: Find total time until they meet", "Let’s determine how long it takes for the trains to cover the 600 km gap:", "[\n\ ext{Time} = \frac{\ ext{Distance}}{\ ext{Speed}} = \frac{600,\ ext{km}}{200,\ ext{km/h}} = 3,\ ext{hours}\n]", "---", "### Step 3: Calculate distance traveled by the first train", "Train A travels at 90 km/h for 3 hours. Distance = speed × time:", "[\n\ ext{Distance} = 90,\ ext{km/h} \ imes 3,\ ext{h} = 270,\ ext{km}\n]", "---", "### Conclusion", "The two trains meet 270 kilometers from the start point of Train A (the faster train, actually — note: Train A indeed starts first and travels 270 km toward the meeting point; Train B starts later but travels 330 km).", "---", "Why this matters:\nUnderstanding relative motion and combined speed helps in many real-world applications—from traffic planning to rescue operations. Solving such problems sharpens analytical thinking and real-time problem-solving skills.", "---", "Keywords for SEO: train meeting point, relative speed calculation, two trains approaching each other, distance traveled by train A, physics distance problem, relative motion solution, traveling towards each other km/h, 600 km train distance."]
