A car travels from City A to City B at a speed of 60 mph and returns at a speed of 40 mph. If the total travel time is 5 hours, what is the distance between the two cities?
["Title: Solving The Classic Travel Time Puzzle: How to Find the Distance Between Two Cities When Speeds Differ", "When calculating distances involving equal routes with different speeds, many people struggle to apply the right formula. A classic example is a car traveling from City A to City B at 60 mph and returning at 40 mph, with a total round-trip time of 5 hours. Understanding how to calculate the distance in such a scenario helps solve both everyday problems and more complex travel calculations.", "---", "### The Problem Explained", "Let the distance between City A and City B be ( D ) miles.", "- Time taken to travel from A to B:\n ( t_1 = \frac{D}{60} ) hours\n- Time taken to return from B to A:\n ( t_2 = \frac{D}{40} ) hours", "Total travel time is given as:\n[ t_1 + t_2 = 5 ]", "Substituting the expressions:\n[ \frac{D}{60} + \frac{D}{40} = 5 ]", "---", "### Solving the Equation", "To combine the terms, find the least common denominator of 60 and 40, which is 120.", "Rewrite the fractions:", "[ \frac{2D}{120} + \frac{3D}{120} = 5 ]\n[ \frac{5D}{120} = 5 ]", "Simplify:", "[ \frac{D}{24} = 5 ]", "Solve for ( D ):", "[ D = 5 \ imes 24 = 120 ]", "---", "### Result", "The distance between City A and City B is 120 miles.", "---", "### Why This Works", "This problem demonstrates the harmonic mean effect, common in average speed calculations with unequal travel speeds. When speeds differ but distance is constant, the average speed isn’t the arithmetic mean but rather depends on equal distance traveled at each speed. The harmonic mean naturally emerges in such scenarios, especially when expressing time-based relationships.", "---", "### Real-World Applications", "This type of problem helps in:", "- Calculating commute times between cities with variable traffic speeds\n- Planning logistics and delivery routes\n- Understanding average speeds for long-distance travel", "---", "### Conclusion", "Next time you encounter a travel time puzzle with different speeds, remember to model the equation using distance = speed × time, combine the segments correctly, and apply algebra step-by-step. In this case, a 120-mile stretch separates City A and City B — a neat result born from combining logic and math.", "Key takeaway:\nIf a car travels from A to B at 60 mph and returns at 40 mph with a total travel time of 5 hours, the one-way distance is 120 miles.", "---", "Keywords: travel time difference, round trip distance, speed and time calculation, harmonic mean travel, city distance puzzle, how to find distance with different speeds, math problem solution"]
