A train travels 150 miles at a speed of 50 mph and then another 200 miles at 80 mph. What is the average speed of the train for the entire journey?

["Train Journey Breakdown: Calculating Average Speed Over Two Legs", "When traveling long distances, understanding average speed is crucial—not just for planning trips, but for evaluating efficiency in transportation. Consider a train journey consisting of two distinct segments: first, a 150-mile leg at 50 mph, followed by a 200-mile stretch at 80 mph. What is the train’s average speed for the entire trip?", "### The Combined Journey", "The total distance covered by the train is:\n150 miles + 200 miles = 350 miles", "The journey proceeds in two parts with different speeds:\n- First leg: 150 miles at 50 mph\n- Second leg: 200 miles at 80 mph", "### Calculating Time for Each Segment", "To compute average speed, it’s essential to determine the total time taken.", "First Segment (150 miles at 50 mph):\nTime = Distance ÷ Speed = 150 ÷ 50 = 3 hours", "Second Segment (200 miles at 80 mph):\nTime = Distance ÷ Speed = 200 ÷ 80 = 2.5 hours", "Total time = 3 hours + 2.5 hours = 5.5 hours", "### Computing Average Speed", "Average speed over a full trip is defined as total distance divided by total time:\n[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}} = \frac{350}{5.5} \approx 63.64\ \ ext{mph}\n]", "### Final Insight", "Although the train travels faster on the second leg, the average speed isn’t simply the arithmetic mean (which would be 65 mph). Instead, it reflects the impact of time spent at each speed relative to distance. Because the slower speed covers more of the journey, the train’s pace is pulled downward overall.", "Conclusion: The train’s average speed for the entire 350-mile journey is approximately 63.6 mph.", "This calculation model applies universally across transport—whether trains, cars, or planes—remaining a foundational concept for calculating travel efficiency and route planning."]