A car travels 150 miles at a speed of 50 mph and then another 100 miles at a speed of 25 mph. What is the average speed of the car for the entire trip?
["Average Speed Calculation: Understanding Total Trip Time and Speed", "When planning road trips or analyzing vehicle performance, understanding average speed is essential. It reflects overall journey efficiency more accurately than simple speed averages. This article explores a practical example involving two segments of a trip — one at 50 mph over 150 miles, and another at 25 mph over 100 miles — to calculate the true average speed for the full journey.", "The Journey Breakdown", "The car travels 150 miles at 50 mph and then continues for another 100 miles at 25 mph. To determine the average speed for the entire trip, we must first compute the total distance and total time.", "---", "Step 1: Calculate Total Distance", "[\n\ ext{Total Distance} = 150 \ ext{ miles} + 100 \ ext{ miles} = 250 \ ext{ miles}\n]", "---", "Step 2: Compute Time for Each Segment", "Using the formula:\n[\n\ ext{Time} = \frac{\ ext{Distance}}{\ ext{Speed}}\n]", "- Time for the first segment:\n[\n\frac{150 \ ext{ miles}}{50 \ ext{ mph}} = 3 \ ext{ hours}\n]", "- Time for the second segment:\n[\n\frac{100 \ ext{ miles}}{25 \ ext{ mph}} = 4 \ ext{ hours}\n]", "---", "Step 3: Total Time of the Trip", "[\n\ ext{Total Time} = 3 \ ext{ hours} + 4 \ ext{ hours} = 7 \ ext{ hours}\n]", "---", "Step 4: Calculate Average Speed", "Average speed is defined as total distance divided by total time:", "[\n\ ext{Average Speed} = \frac{250 \ ext{ miles}}{7 \ ext{ hours}} \approx 35.71 \ ext{ mph}\n]", "---", "Why isn’t it 33.33 mph?", "You might wonder why 33.33 mph (the simple harmonic mean of 50 and 25) isn’t correct. Crucially, average speed is not the arithmetic mean because each segment took different amounts of time. The calculation accounts for the duration spent at each speed, ensuring accuracy.", "---", "Why This Matters", "Knowing the average speed helps drivers estimate travel time, optimize fuel usage, and compare journeys. In this case, even though part of the trip averaged 50 mph, slowdowns significantly reduced overall speed.", "---", "Conclusion", "For a 150-mile leg at 50 mph followed by a 100-mile stretch at 25 mph, the true average speed is approximately 35.71 mph. Always remember to track time and distance individually to calculate accurate averages — especially for trips with variable speeds, enabling smarter planning and dynamic driving strategies.", "---", "Keywords: average speed calculation, average speed formula, car trip speed analysis, 150 miles at 50 mph, 100 miles at 25 mph, travel time calculation, road trip efficiency, speed and distance relation."]
