A train travels from City A to City B at 60 km/h and returns at 90 km/h. What is the average speed for the entire round trip?
["Title: What Is the Average Speed for a Round Trip Train Journey from City A to City B?", "Traveling between two cities by train offers a smooth, efficient journey—but how do you calculate the average speed for the entire trip when speeds vary? In this article, we explore a classic scenario: a train traveling from City A to City B at 60 km/h and returning from City B to City A at 90 km/h. We’ll break down the physics, explain why total distance and total time matter, and reveal the formula for calculating the average speed on a round trip.", "---", "### The Classic Round Trip Speed Problem", "Imagine a train departs City A heading to City B at a steady speed of 60 km/h. After a stop, it returns from City B to City A at 90 km/h. Many wonder: What is the average speed for the entire journey?", "A common misconception is to simply average the two speeds—(60 + 90)/2 = 75 km/h—but this does not reflect the true average speed, which depends on equal distance traveled in both directions.", "---", "### Why Average Speed Isn’t Just the Mean", "Average speed is defined as total distance divided by total time, not the arithmetic mean of speeds. Since the train spends more time traveling from City A to City B at the slower speed, the round trip average lies between, but closer to, the slower value.", "Let’s use a concrete example to clarify.", "---", "### Step-by-Step Calculation", "Suppose the one-way distance between City A and City B is ( D ) kilometers.", "#### 1. Calculate time for each leg:", "- Time from City A to City B:\n [ t_1 = \frac{D}{60} \ ext{ hours} ]\n- Time from City B to City A:\n [ t_2 = \frac{D}{90} \ ext{ hours} ]", "#### 2. Total time for the round trip:\n[ T_{\ ext{total}} = t_1 + t_2 = \frac{D}{60} + \frac{D}{90} ]\nFind a common denominator (180):\n[ T_{\ ext{total}} = \frac{3D}{180} + \frac{2D}{180} = \frac{5D}{180} = \frac{D}{36} \ ext{ hours} ]", "#### 3. Total distance traveled:\n[ D_{\ ext{total}} = D + D = 2D ]", "#### 4. Average speed formula:\n[\n\ ext{Average speed} = \frac{\ ext{Total distance}}{\ ext{Total time}} = \frac{2D}{\frac{D}{36}} = 2D \ imes \frac{36}{D} = 72 \ ext{ km/h}\n]", "---", "### Final Answer", "The average speed for the entire round trip from City A to City B and back at 60 km/h and 90 km/h is:", "> ✅ 72 km/h", "---", "### Why This Matters", "Understanding average speed helps travelers, planners, and engineers evaluate journey efficiency. It shows that inconsistent speeds reduce average speed, even with faster return travel. This principle applies broadly—from car commutes to freight logistics.", "---", "### Summary", "- Average speed = total distance ÷ total time\n- Not the arithmetic mean of speeds\n- For equal distances and speeds, average speed =\n [\n \ ext{Average} = \frac{2 \cdot \ ext{Distance}}{\frac{D}{v_1} + \frac{D}{v_2}} = \frac{2}{\frac{1}{v_1} + \frac{1}{v_2}} \ imes 100\n ]\n With ( v_1 = 60 ) km/h and ( v_2 = 90 ) km/h:\n [\n = \frac{2}{\frac{1}{60} + \frac{1}{90}} = 72 \ ext{ km/h}\n ]", "---", "Keywords: average speed, train travel average speed, round trip speed calculator, classic train speed problem, average speed formula, travel between cities km/h", "Meta Description: Discover how to calculate the correct average speed for a round train journey—from City A to City B at 60 km/h and back at 90 km/h. Learn why 72 km/h is the right answer.", "---", "For more travel speed insights and travel planning tips, explore our guides on average speed, journey planning, and efficient commuting."]
