A train travels from City A to City B at a speed of 80 km/h and returns at a speed of 100 km/h. If the total travel time is 9 hours, what is the distance between the two cities?
["Title: Solving the Train Travel Time Problem: How Far Are City A and City B?", "When planning a round-trip journey by train, understandinG travel times and speeds is essential—especially when the return journey moves faster than the outbound leg. In this scenario, a train travels from City A to City B at 80 km/h and returns from City B to City A at 100 km/h. With a total travel time of 9 hours, what is the distance between these two cities?", "### The Problem: Speed, Time, and Distance", "Let’s break down the journey:", "- Let the distance between City A and City B be D kilometers.\n- Time taken from City A to City B:\n [\n \ ext{Time}_1 = \frac{D}{80} \ ext{ hours}\n ]\n- Time taken from City B to City A:\n [\n \ ext{Time}_2 = \frac{D}{100} \ ext{ hours}\n ]\n- Total travel time:\n [\n \ ext{Time}_1 + \ ext{Time}_2 = 9 \ ext{ hours}\n ]", "So, we can write the equation:\n[\n\frac{D}{80} + \frac{D}{100} = 9\n]", "### Step-by-Step Solution", "1. Find a common denominator for the fractions. The least common multiple of 80 and 100 is 400:\n[\n\frac{D \ imes 5}{400} + \frac{D \ imes 4}{400} = 9\n]", "2. Combine the terms:\n[\n\frac{5D + 4D}{400} = 9\n]\n[\n\frac{9D}{400} = 9\n]", "3. Solve for D:\nMultiply both sides by 400:\n[\n9D = 3600\n]\nThen divide by 9:\n[\nD = \frac{3600}{9} = 400\n]", "### Conclusion", "The distance between City A and City B is 400 kilometers.", "### Why This Matters (SEO-Relevant Keywords)", "- Train travel time calculation\n- Round-trip distance estimation\n- Speed, time, and distance formula\n- How to calculate train journey duration\n- Distance between two cities by train", "This practical math example helps travelers understand journey times, engineers optimize schedules, and educators teach real-world applications of algebra. Whether commuting or planning a trip, knowing how to calculate distance using speed and total time is invaluable.", "Keywords: train travel time, City A to City B distance, round trip train speed 80 vs 100 km/h, how to calculate train journey time, D city distance formula, 80 to 100 km/h train math."]
