A car travels at a constant speed. It takes 3 hours to go from City A to City B, and on the return trip, it takes 2 hours. If the total round-trip distance is 500 km, what is the average speed for the entire journey?

["Title: How to Calculate Average Speed for a Round-Trip Journey at Constant Speeds – Analyzing a 3-Hour and 2-Hour Trip", "---", "", "When driving between two cities, understanding average speed for the full journey is essential—especially when travel times differ on the outbound and return trips. In this article, we explore a real-world example: a car travels from City A to City B at a constant speed, taking 3 hours, then returns at a faster constant speed in 2 hours. With a total round-trip distance of 500 km, we calculate the average speed to reveal both the total trip dynamics and key insights for efficient travel planning.", "---", "### The Problem: Constant Speed, Different Times", "- Outbound trip (City A → City B): 3 hours\n- Return trip (City B → City A): 2 hours\n- Total time: 3 + 2 = 5 hours\n- Total distance: 500 km (round trip)\n- Question: What is the average speed for the entire journey?", "---", "### Understanding Average Speed", "Average speed over a round trip is defined as total distance traveled divided by total time taken:", "[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}}\n]", "In this case:", "[\n\ ext{Average Speed} = \frac{500 \ ext{ km}}{5 \ ext{ hours}} = 100 \ ext{ km/h}\n]", "This simple formula captures how time and distance combine to shape overall efficiency in travel.", "---", "### Why Speed Varies Between Trips?", "Even though the problem specifies constant speed for each leg, the speed differs because travel times vary. On the return trip, covering the same 500 km distance in just 2 hours implies a higher speed than the outbound leg.", "- Since total time is 5 hours and total distance is 500 km, dividing gives 100 km/h—your average speed.", "---", "### The Step-by-Step Breakdown", "1. Confirm total time:\n $3 + 2 = 5$ hours\n2. Confirm total distance:\n $500$ km (one way) so round trip = $500 \ imes 2 = 1000$ km? Wait!\n But the problem states 500 km round trip, meaning total distance traveled between City A and City B is 500 km one way, so the full round trip distance is indeed 500 km (one way only). However, standard interpretation interprets “round-trip distance” as total round trip, or total distance traveled between start and finish over the cycle.", "Critical clarification:\n - If “500 km total round-trip distance” means round trip, total distance should be 500 km (approximately one-way is 250 km).\n - But most consistent interpretation (especially in travel contexts) treats the “round trip distance” as total round journey, so if total round distance is 500 km, then total round distance is 500 km across the 5-hour cycle — i.e., one-way 250 km, total out and back 500 km.", "However, the correct physical interpretation is:\n - Distance from A to B = 250 km (one way)\n - Return trip also 250 km\n - But given trip times suggest average speed based on total distance traveled in 5 hours.", "But the problem says: “the total round-trip distance is 500 km.” This implies round-trip distance, so the car travels 500 km total (250 to, 250 back).", "Correction: If the round-trip distance is 500 km, and it takes 5 hours total, average speed is:", "[\n \ ext{Average Speed} = \frac{500 \ ext{ km}}{5 \ ext{ hours}} = 100 \ ext{ km/h}\n ]", "Thus, average speed is 100 km/h, regardless of speed variations on each leg.", "---", "### Real-World Application of Average Speed", "In vehicle travel, average speed provides a holistic measure of journey efficiency, important for fuel consumption, scheduling, and logistics. When traveling at constant speeds on each leg, even if speeds differ, the overall average speed depends only on total distance and total time.", "---", "### Bonus: Calculating Individual Speeds (Optional)", "Let’s find the constant speeds on each trip:", "- Let distance from A to B be ( d = 250 ) km\n- Outbound speed: ( v_1 = \frac{d}{3} = \frac{250}{3} \approx 83.33 ) km/h\n- Return speed: ( v_2 = \frac{d}{2} = \frac{250}{2} = 125 ) km/h\n- Total: ( 83.33 + 125 = 208.33 ) km (nonsensical—total distance isn’t sum)", "Wait! Clarify: The round trip is 500 km total (e.g., 250 km one-way), so each leg is 250 km.", "But the total distance is 500 km for the round trip, but path is 250 km × 2 = 500 km.", "So:", "- Trip 1 (A to B): 250 km in 3 hours → speed = ( \frac{250}{3} \approx 83.33 ) km/h\n- Trip 2 (B to A): 250 km in 2 hours → speed = ( \frac{250}{2} = 125 ) km/h", "Thus, the car adjusted speed between segments to complete the 5-hour round trip efficiently.", "---", "### Final Answer", "The average speed for the entire round-trip journey is:", "[\n\boxed{100 \ ext{ km/h}}\n]", "---", "### Key Takeaways", "- Average speed = total distance ÷ total time\n- Variations in speed between segments don’t require averaging individual speeds unless calculating fuel or time efficiency per segment\n- Clarifying whether “round-trip distance” refers to one-way or full round is critical\n- Even with uneven travel times, consistent distance and total time simplify average speed calculation", "Understanding average speed empowers smarter travel decisions—whether you're commuting, planning road trips, or optimizing delivery routes.", "---", "Keywords: Average speed, round-trip average speed, constant speed journey, speed calculation, travel time, distance and speed, vehicle journey analysis, average speed formula, round trip 500 km, time-distance relationship.", "Self-optimizing Content — tailored to common search intent and precise, accurate AP Q&A format."]