A train travels from City A to City B at a speed of 80 miles per hour and returns at a speed of 60 miles per hour. If the total travel time for the round trip is 7 hours, what is the distance between City A and City B?
["Title: Solving a Classic Train Round-Trip Problem: How Far Are City A and City B?", "When planning a journey or solving transportation problems, one common equation involves speed, distance, and time. A real-life scenario that illustrates this is a train traveling from City A to City B at 80 mph and returning at 60 mph, with the total round-trip time amounting to 7 hours. Using this setup, determining the distance between the two cities becomes both practical and mathematically engaging.", "---", "### Understanding the Journey", "Let the distance between City A and City B be D miles.", "- On the outbound trip (A → B), the train travels at 80 mph, so the time taken is ( \frac{D}{80} ) hours.\n- On the return trip (B → A), with a speed of 60 mph, the time is ( \frac{D}{60} ) hours.", "The total travel time for the round trip is given as 7 hours, so we can write:", "[\n\frac{D}{80} + \frac{D}{60} = 7\n]", "---", "### Solving for Distance D", "To solve this equation, first find a common denominator for the fractions. The least common multiple of 80 and 60 is 240:", "[\n\frac{3D}{240} + \frac{4D}{240} = 7\n]", "Add the numerators:", "[\n\frac{7D}{240} = 7\n]", "Multiply both sides by 240:", "[\n7D = 7 \ imes 240\n]", "[\n7D = 1680\n]", "Divide both sides by 7:", "[\nD = \frac{1680}{7} = 240\n]", "---", "### Final Answer", "The distance between City A and City B is 240 miles.", "This means the train covers 240 miles each way, and due to unequal speeds, the return journey takes longer—adding up to exactly 7 hours. This classic example reinforces the value of the average speed for round trips and highlights how differing velocities impact travel time.", "---", "### Why This Problem Matters", "Beyond exercise, understanding round-trip scenarios helps in logistics, commute planning, and transportation analysis. Whether you're commuting, shipping goods, or analyzing train schedules, calculating distance using variable speeds ensures accurate estimations and better decision-making.", "---", "Keywords: train travel time, round trip distance calculation, average speed problem, public transportation speed, City A to City B distance, math problem solution, speed and time formula", "Meta Description:\nDiscover how to calculate the distance between two cities using a train’s round-trip speeds (80 mph out, 60 mph return) with a total travel time of 7 hours. Step-by-step solution with formula and explanation."]
