A car travels from City A to City B at an average speed of 60 km/h and returns at an average speed of 80 km/h. If the total travel time is 7 hours, what is the distance between the two cities?
["Title: Calculating the Distance Between Two Cities Based on Average Speeds and Total Travel Time", "When planning a road trip, understanding how travel speed affects total journey time is essential—especially when the return trip differs in speed. In this article, we explore a common physics and travel planning problem: a car traveling from City A to City B at 60 km/h and returning at 80 km/h, with a total round-trip time of 7 hours. We’ll determine the distance between the two cities using average speed and time concepts.", "---", "### Problem Setup", "Let the distance between City A and City B be ( d ) kilometers.", "- Time taken to travel from City A to City B:\n [\n t_1 = \frac{d}{60} \ ext{ hours}\n ]", "- Time taken to return from City B to City A:\n [\n t_2 = \frac{d}{80} \ ext{ hours}\n ]", "- Total travel time is 7 hours:\n [\n t_1 + t_2 = 7\n ]", "---", "### Step-by-Step Solution", "Start with the equation:\n[\n\frac{d}{60} + \frac{d}{80} = 7\n]", "To combine the fractions, find a common denominator. The least common multiple of 60 and 80 is 240:", "[\n\frac{4d}{240} + \frac{3d}{240} = 7\n]", "[\n\frac{7d}{240} = 7\n]", "Multiply both sides by 240:\n[\n7d = 1680\n]", "Divide both sides by 7:\n[\nd = 240\n]", "---", "### Conclusion", "The distance between City A and City B is 240 kilometers.", "---", "### Bonus Explanation: Why Does This Work?", "Using harmonic mean for average speed over equal distances, the overall average speed is:", "[\n\ ext{Average Speed} = \frac{2 \ imes 60 \ imes 80}{60 + 80} = \frac{9600}{140} \approx 68.57 \ ext{ km/h}\n]", "Then, total time = ( \frac{2d}{68.57} = 7 ) hours →\n( d = \frac{7 \ imes 68.57}{2} \approx 240 ) km, confirming our result.", "---", "### SEO Keywords & Meta Description", "Keywords:\nCity A to City B distance, average speed travel time, round trip speed calculation, 60 km/h to 80 km/h return journey", "Meta Description:\nDiscover how to calculate the distance between two cities using average speeds and total travel time. Example: a car traveling 60 km/h to City B and 80 km/h back with a combined 7-hour trip covers 240 km.", "---", "Optimizing for search engines and clear explanations helps travelers, students, and planners understand real-world route calculations—whether for commuting, logistics, or personal trips."]
