A car travels from point A to point B at a speed of 60 km/h and returns at a speed of 80 km/h. If the total travel time is 7 hours, what is the distance between points A and B?
["Title: Solve the Classic Travel Time Problem: Find the Distance Between Points A and B", "Meta Description: Discover how to calculate the distance between two points when a car travels at 60 km/h to and 80 km/h on the return trip, with a total travel time of 7 hours. Step-by-step solution explained.", "---", "When a car journeys from Point A to Point B and back, traveling at different speeds, determining the distance between the two points becomes an engaging math challenge. This problem is a classic example often used in algebra and physics—balancing speed, time, and distance. In this article, we’ll solve the scenario where a car travels from A to B at 60 km/h and returns at 80 km/h, completing the round trip in exactly 7 hours. We’ll walk through how to find the distance between the two points.", "---", "### The Problem Recap", "- Speed from A to B = 60 km/h\n- Speed from B to A = 80 km/h\n- Total travel time = 7 hours\n- Distance from A to B = Distance from B to A = ( d ) km (let’s call it ( d ))", "We need to find ( d ), the distance between Points A and B.", "---", "### Step-by-Step Solution", "Step 1: Express time taken for each leg of the journey", "Time = Distance ÷ Speed", "- Time from A to B = ( \frac{d}{60} ) hours\n- Time from B to A = ( \frac{d}{80} ) hours", "Step 2: Set up the equation using total travel time", "The total time is the sum of both trips:\n[\n\frac{d}{60} + \frac{d}{80} = 7\n]", "Step 3: Solve for ( d )", "First, find a common denominator for 60 and 80. The least common multiple of 60 and 80 is 240. Rewrite each fraction:", "[\n\frac{d}{60} = \frac{4d}{240}, \quad \frac{d}{80} = \frac{3d}{240}\n]", "Now substitute into the equation:", "[\n\frac{4d}{240} + \frac{3d}{240} = 7\n]\n[\n\frac{7d}{240} = 7\n]", "Multiply both sides by 240:", "[\n7d = 7 \ imes 240\n]\n[\n7d = 1680\n]", "Divide both sides by 7:", "[\nd = \frac{1680}{7} = 240\n]", "---", "### Final Answer", "The distance between Points A and B is 240 kilometers.", "---", "### Bonus Insight: Why This Problem Matters", "This problem beautifully illustrates the relationship between speed, distance, and time. By working through it, you strengthen your problem-solving skills in algebra and prepare for real-world scenarios—such as optimizing travel plans, calculating logistics, or understanding vehicular efficiency.", "Whether you're a student, a teacher, or someone curious about practical math, solving such problems sharpens logic and analytical thinking.", "---", "Keywords: car travel time problem, how to find distance with two speeds, travel distance calculation, speed and time formula, 60 km/h to 80 km/h round trip, distance between two points formula", "IBM Keywords: car speed time distance, round trip distance problem, math word problem 2024, algebra travel distance, average speed round trip solution"]
