If a train travels 180 miles in 3 hours, what is the average speed in miles per hour? If the train then travels an additional 120 miles at the same speed, how much total time will it take for both journeys?
["Average Speed and Total Travel Time: Understanding Train Journey Speeds", "When analyzing train travel, understanding average speed and total journey time is essential for planning and efficiency. Let’s break down one common calculation: if a train travels 180 miles in 3 hours, what is its average speed in miles per hour? Then, we’ll explore how much total time it takes when the train continues for an additional 120 miles at the same speed.", "Calculating Average Speed", "Average speed measures distance traveled divided by time taken. Using the formula:", "[\n\ ext{Average Speed} = \frac{\ ext{Distance}}{\ ext{Time}}\n]", "For the first leg of the journey:", "[\n\ ext{Distance} = 180 \ ext{ miles}, \quad \ ext{Time} = 3 \ ext{ hours}\n]", "[\n\ ext{Average Speed} = \frac{180 \ ext{ miles}}{3 \ ext{ hours}} = 60 \ ext{ miles per hour (mph)}\n]", "So, the train travels at an average speed of 60 mph.", "Total Travel Time for Both Journeys", "If the train maintains the same 60 mph speed for the next leg—120 miles—the time required is:", "[\n\ ext{Time} = \frac{\ ext{Distance}}{\ ext{Speed}} = \frac{120 \ ext{ miles}}{60 \ ext{ mph}} = 2 \ ext{ hours}\n]", "Adding both journeys:", "- First leg: 3 hours\n- Second leg: 2 hours", "[\n\ ext{Total Travel Time} = 3 + 2 = 5 \ ext{ hours}\n]", "Conclusion", "A train moving consistently at 60 miles per hour covers 180 miles in 3 hours and an additional 120 miles in 2 hours, resulting in a total travel time of 5 hours. Mastering speed calculations helps optimize scheduling and travel planning, especially for long-distance train routes. Always verify speed consistency to estimate travel times accurately."]
