A train travels 300 miles at a speed of 60 mph, then continues for another 200 miles at 80 mph. What is the train's average speed for the entire journey?

["Title: What Is the Average Speed of a Train Traveling 300 Miles at 60 mph and 200 Miles at 80 mph?", "When planning a long-distance train journey, one key question often arises: What is the average speed for the entire trip? In this article, we explore a practical scenario involving a train traveling two distinct segments — 300 miles at 60 mph, followed by 200 miles at 80 mph — and calculate the overall average speed using honest physics and math.", "### The Journey Breakdown", "The train’s trip consists of two phases:", "1. First Segment:\n - Distance: 300 miles\n - Speed: 60 mph\n - Time = Distance ÷ Speed = 300 ÷ 60 = 5 hours", "2. Second Segment:\n - Distance: 200 miles\n - Speed: 80 mph\n - Time = 200 ÷ 80 = 2.5 hours", "### Total Distance and Total Time", "- Total distance:\n 300 miles + 200 miles = 500 miles\n- Total time:\n 5 hours + 2.5 hours = 7.5 hours", "### Calculating Average Speed", "Average speed is defined as the total distance traveled divided by the total time taken:", "[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}} = \frac{500 \ ext{ miles}}{7.5 \ ext{ hours}} \approx 66.67 \ ext{ mph}\n]", "### Why This Matters", "Many assume the average speed is simply the arithmetic mean of 60 mph and 80 mph — which would be (60 + 80) ÷ 2 = 70 mph. However, because the train spends more time at the slower speed, the overall average is pulled down — confirming it’s not 70 mph, but 60 + 66.67 = 126.67 ÷ 2 ≈ 63.3 mph? Wait — no. Actually, we used the actual route and time, confirming the correct average is ≈ 66.67 mph. The key takeaway is that average speed accounts for varying speeds, not average of speeds.", "### Conclusion", "The train’s average speed over the full 500-mile journey is approximately 66.7 mph, demonstrating how longer segments at slower speeds significantly impact overall efficiency. Understanding this helps passengers and planners better anticipate travel times and optimize railway network performance.", "Key Takeaway:\nTo calculate average speed over multiple segments, always divide total distance by total time — not the average of speeds. This principle applies not just to trains, but to all multi-segment journeys."]