A train travels 300 km at a speed of 100 km/h, then continues another 200 km at 80 km/h. What is the average speed for the entire journey?
["Title: How to Calculate Average Speed for a Train Journey: A Practical Example", "When planning or analyzing train travel, understanding average speed is essential. It helps travelers estimate arrival times and assess journey efficiency. In this article, we break down a real-world scenario: a train journey covering 300 km at 100 km/h followed by an additional 200 km at 80 km/h. We’ll calculate the average speed for the entire trip and explain the key concepts behind the formula.", "---", "### The Journey Overview\n- First leg: 300 kilometers at a speed of 100 km/h\n- Second leg: 200 kilometers at a speed of 80 km/h", "At first glance, average speed may seem like a simple average of 100 km/h and 80 km/h:\n[\n\frac{100 + 80}{2} = 90 \ ext{ km/h}\n]\nHowever, this arithmetic average doesn’t account for time spent on each segment, and it's not the correct method for calculating average speed over variable-distance journeys.", "---", "### Understanding Average Speed\nAverage speed is defined as the total distance traveled divided by the total time taken over the entire journey. Unlike constant speed, average speed in multi-segment trips depends on the time spends in each part of the trip.", "---", "### Step-by-Step Calculation", "#### 1. Calculate time for each leg\n- First leg:\n Distance = 300 km, Speed = 100 km/h\n [\n \ ext{Time}_1 = \frac{\ ext{Distance}}{\ ext{Speed}} = \frac{300}{100} = 3 \ ext{ hours}\n ]", "- Second leg:\n Distance = 200 km, Speed = 80 km/h\n [\n \ ext{Time}_2 = \frac{200}{80} = 2.5 \ ext{ hours}\n ]", "#### 2. Total distance and total time\n- Total distance = 300 km + 200 km = 500 km\n- Total time = 3 hours + 2.5 hours = 5.5 hours", "#### 3. Compute average speed\n[\n\ ext{Average speed} = \frac{\ ext{Total distance}}{\ ext{Total time}} = \frac{500}{5.5} \approx 90.91 \ ext{ km/h}\n]", "---", "### Final Insight\nThe average speed of the train journey is approximately 90.91 km/h, significantly higher than either 100 km/h or 80 km/h due to the longer duration of the slower second leg.", "---", "### Why This Matters\nKnowing the true average speed helps passengers and schedulers:\n- Predict arrival times more accurately\n- Evaluate route efficiency\n- Compare different transportation options", "---", "In summary: To find the average speed on a journey with varying speeds, calculate time for each segment, sum distances and times, then divide total distance by total time. Mastering this simple yet powerful formula enhances travel planning and understanding of motion dynamics.", "Keywords: average speed formula, train journey calculation, average speed average h, distance and time, travel time calculation"]
