A train travels from City A to City B at an average speed of 80 km/h and returns at an average speed of 100 km/h. If the total travel time for the round trip is 9 hours, what is the distance between City A and City B?

["Title: Solving the Round-Trip Train Travel Problem: How Far is City A from City B?", "Travel planning often involves understanding travel times, speeds, and distances—especially when trains make round trips with different speeds on each leg. In this insightful analysis, we uncover the mystery behind the distance between City A and City B when a train travels from City A to City B at 80 km/h and returns at 100 km/h, with the total round trip taking 9 hours.", "---", "### The Math Behind the Round Trip", "Let the one-way distance between City A and City B be D kilometers.", "- On the outbound journey, speed = 80 km/h, so travel time = D / 80 hours.\n- On the return journey, speed = 100 km/h, so travel time = D / 100 hours.", "The total time for the round trip is given as 9 hours:", "[\n\frac{D}{80} + \frac{D}{100} = 9\n]", "---", "### Solving the Equation", "To solve, first find a common denominator for 80 and 100. The least common multiple of 80 and 100 is 400.", "[\n\frac{5D}{400} + \frac{4D}{400} = 9\n]\n[\n\frac{9D}{400} = 9\n]", "Multiply both sides by 400:", "[\n9D = 3600\n]", "Divide both sides by 9:", "[\nD = 400\n]", "---", "### Conclusion", "The distance between City A and City B is 400 kilometers. This elegant round-trip problem demonstrates how average speeds differ on each leg and how total travel time helps solve for unknown distances efficiently.", "Whether you're commuting, planning a trip, or tackling a logic puzzle, understanding the relationship between speed, time, and distance is key—and today’s example proves it with clarity.", "---", "Key keywords: train travel distance, round-trip train speed, average speed calculation, train travel time problem, City A to City B distance, solve train round trip, distance between two cities formula."]