Question:** A car travels 150 miles at a speed of 50 mph, then 200 miles at 40 mph. What is the average speed for the entire trip?
["Average Speed for a Car Trip: Understanding Total Distance vs. Total Time", "When planning a long drive, one common question drivers ask is: What is the average speed for my entire trip? Understanding average speed helps travelers estimate arrival times, plan fuel stops, and gain clarity on journey efficiency.", "### Calculating Average Speed: The Correct Formula", "Average speed isn’t simply the mean of two speeds, because the time spent traveling at each speed matters. The correct formula for average speed over a trip is:", "[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}}\n]", "### Step-by-step Breakdown of the Example", "Let’s analyze the scenario:\n- First leg: 150 miles at 50 mph\n- Second leg: 200 miles at 40 mph", "1. Calculate time for each segment", "- Time = Distance ÷ Speed\n- Time for first leg: ( \frac{150 \ ext{ miles}}{50 \ ext{ mph}} = 3 \ ext{ hours} )\n- Time for second leg: ( \frac{200 \ ext{ miles}}{40 \ ext{ mph}} = 5 \ ext{ hours} )", "2. Find total distance and total time\n- Total distance = 150 + 200 = 350 miles\n- Total time = 3 + 5 = 8 hours", "3. Compute average speed\n[\n\ ext{Average Speed} = \frac{350 \ ext{ miles}}{8 \ ext{ hours}} = 43.75 \ ext{ mph}\n]", "### Why This Matters", "The average speed of 43.75 mph is lower than either leg’s speed because the car spent more time on the slower segment (200 miles at 40 mph). This example illustrates how varying speeds affect overall journey performance and why direct speed averaging fails to reflect reality.", "### Takeaway", "To find the average speed for any multi-stage trip:", "- Calculate time for each segment using distance and speed\n- Add total distances and total times\n- Divide total distance by total time", "Understanding this concept helps drivers make smarter decisions on the road—whether estimating travel time or optimizing fuel stops.", "---", "Keywords: average speed calculation, average speed formula, car trip journey time, driving journey average speed, average speed for multi-leg trip, travel time calculation, speed vs time average"]
