A car travels from City A to City B, a distance of 300 km, at an average speed of 60 km/h. Then, it returns to City A at an average speed of 75 km/h. What is the average speed for the entire trip?
["Optimize Your Road Trip: Calculating Average Speed for a Round-Trip Journey Between Two Cities", "Planning a road trip from City A to City B and back? Whether you're commuting, exploring, or running errands, understanding your average speed is key to estimating travel time and improving efficiency. In this article, we’ll explore a common scenario: a 300 km journey from City A to City B at an average speed of 60 km/h, followed by a return trip at 75 km/h. We’ll explain how to calculate the overall average speed for the complete round trip and why it matters.", "---", "### The Journey Overview", "- One-way distance: 300 km\n- First leg (City A → City B): Speed = 60 km/h\n- Return leg (City B → City A): Speed = 75 km/h", "At first glance, it might seem the average speed is simply the mean of 60 and 75 — but that’s only an approximation. true average speed depends on equal time allocation or equal distance — because speed is a ratio of distance to time.", "---", "### Step 1: Calculate Travel Time for Each Leg", "Outbound (City A to City B):\nTime = Distance ÷ Speed = 300 km ÷ 60 km/h = 5 hours", "Return (City B to City A):\nTime = 300 km ÷ 75 km/h = 4 hours", "---", "### Step 2: Total Distance and Total Time", "- Total distance = 300 km + 300 km = 600 km\n- Total time = 5 hours + 4 hours = 9 hours", "---", "### Step 3: Calculate Average Speed", "Average speed is defined as total distance divided by total time:", "[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}} = \frac{600\ \ ext{km}}{9\ \ ext{h}} = 66.\overline{6}\ \ ext{km/h}\n]", "So, the overall average speed for the round trip is approximately 66.7 km/h, or roughly 66.7 km/h.", "---", "### Why This Difference from the Simple Average?", "You might expect:\n[\n\frac{60 + 75}{2} = 67.5\ \ ext{km/h}\n]", "But because the trip spends more time at the slower speed (60 km/h), the overall average is pulled down — reflecting the mathematical principle that equal time intervals make the harmonic mean the correct average for average speed on equal distances.", "---", "### Practical Takeaways", "- Average speed for round trips isn’t just arithmetic mean unless trip durations are equal.\n- Knowing average speed helps with realistic travel planning, fuel estimation, and schedule setting.\n- For long-distance travelers, monitoring real-time speeds and adjusting routes accordingly maximizes efficiency.", "---", "Next time you plan a trip across 300 km and beyond, remember: the average speed across your entire journey is 66.7 km/h, not 67.5 km/h — a small difference but meaningful in planning.", "---", "Keywords: average speed round trip, car journey calculation, how to calculate average speed, road trip planning, 300 km travel time, average speed formula, travel time optimization, fuel efficiency planning"]
