A train travels 180 miles at a speed of 60 mph, then another 120 miles at 80 mph. What is the average speed for the entire journey?
["# Understanding Average Speed: A Train Journey Analysis", "When planning or analyzing travel times, one of the most important metrics is average speed—a key factor that helps travelers estimate journey duration and compare different routes. In this article, we’ll explore a practical example: a train covering 180 miles at 60 mph, then another 120 miles at 80 mph, and discover the true average speed for the full journey.", "## The Journey Breakdown", "Let’s break down the train’s trip step by step:", "- First leg:\n Distance = 180 miles\n Speed = 60 mph\n Time = Distance ÷ Speed = 180 ÷ 60 = 3 hours", "- Second leg:\n Distance = 120 miles\n Speed = 80 mph\n Time = 120 ÷ 80 = 1.5 hours", "### Total Distance Covered\n180 miles + 120 miles = 300 miles", "### Total Time Taken\n3 hours + 1.5 hours = 4.5 hours", "## Calculating the Average Speed", "Average speed is calculated by dividing total distance by total time:", "[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}} = \frac{300\ \ ext{miles}}{4.5\ \ ext{hours}} = 66.67\ \ ext{mph}\n]", "So, the average speed for the entire journey is approximately 66.67 mph.", "## Why Average Speed Matters", "Unlike simple speed calculations, average speed reflects the actual pace of a journey involving variable speeds—common in real-world travel. It helps passengers manage expectations, schedule arrivals accurately, and compare train routes more effectively.", "## Conclusion", "Understanding how to compute average speed enriches your travel planning skills. In this journey—180 miles at 60 mph and 120 miles at 80 mph—the average speed comes out to about 66.67 mph, underscoring how fluctuating speeds impact overall journey time. Whether you’re a traveler, commuter, or logistics enthusiast, mastering average speed calculations ensures smoother, better-informed travel experiences.", "Key takeaway:\nAverage speed = Total Distance ÷ Total Time — a formula that simplifies complex journeys into clear, actionable insights."]
