A train travels from City A to City B at 60 km/h and returns at 40 km/h. The total travel time is 5 hours. What is the distance between the two cities?
["Title: Solving a Classic Train Travel Problem: Distance Between Two Cities Traveled at Different Speeds", "Traveling between two cities by train often raises a common yet intriguing question: If a train travels from City A to City B at 60 km/h and returns at 40 km/h, with the total round-trip time equal to 5 hours, what is the distance between them? This classic problem combines algebra and real-world travel dynamics, making it a great exercise in logic and problem-solving.", "In this article, we break down the math behind this scenario and reveal how to accurately calculate the distance.", "---", "### Understanding the Scenario", "- Speed from City A to City B: 60 km/h\n- Speed from City B to City A (return trip): 40 km/h\n- Total round-trip travel time: 5 hours", "Let the distance between City A and City B be d kilometers.", "---", "### Step-by-Step Calculation", "1. Time taken to travel from City A to City B:\n Time = Distance ÷ Speed\n ( t_1 = \frac{d}{60} ) hours", "2. Time taken to return from City B to City A:\n ( t_2 = \frac{d}{40} ) hours", "3. Total travel time is 5 hours:\n ( t_1 + t_2 = 5 )\n ( \frac{d}{60} + \frac{d}{40} = 5 )", "4. Find a common denominator:\n The least common multiple of 60 and 40 is 120. Rewrite the equation:\n ( \frac{2d}{120} + \frac{3d}{120} = 5 )\n ( \frac{5d}{120} = 5 )", "5. Solve for d:\n Multiply both sides by 120:\n ( 5d = 600 )\n ( d = \frac{600}{5} = 120 )", "---", "### Final Answer", "The distance between City A and City B is 120 kilometers.", "---", "### Why This Problem Matters (Practical Insights)", "Understanding average speed for round trips helps in logistics, scheduling, and travel planning. Even if a train doesn’t travel the same distance at the same speed each way, knowing how distance responds to varying speeds is crucial for accurate time estimation.", "---", "### Key Takeaway", "Given unequal speeds on a round trip, the distance can be found using:\n[\nd = \frac{t_{\ ext{total}} \ imes v_1 \ imes v_2}{v_1 + v_2}\n]\nFor this case:\n[\nd = \frac{5 \ imes 60 \ imes 40}{60 + 40} = \frac{12000}{100} = 120 \ ext{ km}\n]", "---", "Whether you're planning a train journey or solving this type of puzzle, knowing how average speed depends on speed and distance ensures smarter travel decisions. Next time you see a train traveling between two cities at differing speeds, you’ll instantly recognize how simple algebra unveils the hidden truth — the distance is 120 km!", "---", "Keywords: train travel distance calculation, average speed round trip, train route problem solution, City A to City B speed math, 60 km/h vs 40 km/h train time, how to find distance train journey", "Meta Description: Discover how to calculate the distance between two cities when a train travels at 60 km/h one way and 40 km/h return, with a total travel time of 5 hours. Learn the step-by-step math."]
