A train travels from City A to City B at a constant speed of 80 km/h. After a 1-hour stop in City B, it returns to City A at a speed of 100 km/h. The round trip takes 9 hours. What is the distance between City A and City B?
["Title: Solve the Train Journey Puzzle: How to Find the Distance Between City A and City B", "If you've ever pondered a classic train journey problem involving constant speeds, stopovers, and round-trip timing, you're in the right place. Let’s unpack a real-world travel riddle: a train traveling between two cities under specific conditions, and discover the exact distance between City A and City B.", "---", "### The Journey Overview", "A train departs City A and travels to City B at a steady speed of 80 km/h. It arrives and stops for 1 hour in City B. Then, it returns to City A at a faster speed of 100 km/h. The entire round trip—including the stop—takes precisely 9 hours.", "Question: What is the distance between City A and City B?", "What seems like a complex problem simplifies beautifully with basic algebra and an understanding of time = distance ÷ speed.", "---", "### Break Down the Trip", "Let’s define the unknown distance as D (in km).", "#### Outbound leg: City A → City B\n- Speed = 80 km/h\n- Distance = D km\n- Time = ( \frac{D}{80} ) hours", "#### Stop in City B\n- Time = 1 hour", "#### Return leg: City B → City A\n- Speed = 100 km/h\n- Distance = D km\n- Time = ( \frac{D}{100} ) hours", "---", "### Total Time Equation", "Total round trip time equals 9 hours:", "[\n\frac{D}{80} + 1 + \frac{D}{100} = 9\n]", "Subtract 1 from both sides:", "[\n\frac{D}{80} + \frac{D}{100} = 8\n]", "Find a common denominator for the left-hand side — the least common multiple of 80 and 100 is 400.", "[\n\frac{5D}{400} + \frac{4D}{400} = 8\n]", "[\n\frac{9D}{400} = 8\n]", "Multiply both sides by 400:", "[\n9D = 3200\n]", "Divide both sides by 9:", "[\nD = \frac{3200}{9} \approx 355.56 \ ext{ km}\n]", "---", "### Final Answer", "The distance between City A and City B is (\frac{3200}{9}) kilometers, or approximately 355.56 km.", "---", "### Bonus Insight", "This problem illustrates how understanding speed, time, and distance relationships enables precise travel planning and logistical optimization—key skills in transportation and scheduling. Whether for commuters, logistics planners, or curious minds, mastering such puzzles enhances problem-solving abilities used in real transportation networks.", "---", "Keywords for SEO:\nTrain journey time calculation, round trip train speed problem, distance between two cities, algebraic travel puzzle, 80 km/h train, 100 km/h train round trip, how to calculate train travel distance, train stopover time calculation, 9-hour train trip problem", "Meta Description:\nFind the distance between City A and City B given a train travels at 80 km/h to City B, stops for 1 hour, then returns at 100 km/h, with a total round trip of 9 hours. Solve the puzzle using time, speed, and distance equations."]
