A car travels from city A to city B at 60 km/h and returns at 40 km/h. What is the average speed for the entire round trip?
["Title: Average Speed for a Round Trip: Traveling City A to City B at 60 km/h and Return at 40 km/h", "---", "When thinking about travel between two cities, speed matters—but the real crux often lies not in individual speeds, but in the average speed for the entire journey. A common challenge that puzzles many is calculating the average speed when a car travels a distance from City A to City B at one speed and returns at a different speed. Let’s solve this classic problem with a clear, step-by-step approach.", "### The Problem Recap", "A car travels from City A to City B at 60 km/h, then returns from City B to City A at 40 km/h. What is the average speed for the full round trip?", "---", "### Why Average Speed Isn’t Just the Average of the Two Speeds", "Many beginners assume that simply averaging 60 km/h and 40 km/h gives the correct average speed. However, this is incorrect because the car spends more time traveling at the slower speed. The average speed must account for both journey times and distances equally.", "### Step-by-Step Calculation", "Let’s assume the distance between City A and City B is D kilometers.", "---", "Step 1: Calculate time for each leg of the trip", "- Time from A to B:\n [\n \ ext{Time}{AB} = \frac{\ ext{Distance}}{\ ext{Speed}} = \frac{D}{60} \ ext{ hours}\n ]", "- Time from B to A:\n [\n \ ext{Time}} = \frac{D}{40} \ ext{ hours\n ]", "---", "Step 2: Compute total distance and total time", "- Total distance:\n [\n D + D = 2D \ ext{ km}\n ]", "- Total time:\n [\n \ ext{Time}_{\ ext{total}} = \frac{D}{60} + \frac{D}{40}\n ]", "To add the fractions, find a common denominator:\n[\n\frac{D}{60} + \frac{D}{40} = \frac{2D}{120} + \frac{3D}{120} = \frac{5D}{120} = \frac{D}{24} \ ext{ hours}\n]", "---", "Step 3: Compute average speed", "Average speed is total distance divided by total time:\n[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}} = \frac{2D}{\frac{D}{24}} = 2D \cdot \frac{24}{D} = 48 \ ext{ km/h}\n]", "---", "### Final Answer", "The average speed for the entire round trip from City A to City B and back is 48 km/h.", "---", "### Key Takeaways", "- Average speed ≠ arithmetic mean of speeds when distances are equal but speeds differ.\n- Time spent at slower speeds significantly impacts overall average speed.\n- Always calculate each leg’s time separately and sum them to find total time.\n- This formula applies broadly in travel planning, logistics, and transportation studies.", "---", "For smarter travel choices, remember: distance × average speed reveals true journey efficiency—whether commuting daily, planning a road trip, or optimizing freight routes.", "---", "Keywords: average speed round trip, average speed car travel, math problem average speed city A to city B, journey average speed formula, 60 km/h to 40 km/h average\nMeta Description: Discover how to calculate the correct average speed for a round trip when driving at different speeds — with real calculation and physics behind the result. Learn why average speed is distance over total time."]
