A car travels 150 km in 2 hours and then 90 km in 1.5 hours. What is the average speed for the entire trip?
["Total Distance and Average Speed: Understanding a Car’s Trip from 150 km and 90 km Travel", "When analyzing any road trip, one key question often arises: what was the average speed for the entire journey? This metric helps travelers understand journey efficiency, compare travel times, and plan future routes. Let’s explore a specific trip scenario — a car traveling 150 kilometers in 2 hours, followed by 90 kilometers in 1.5 hours — and calculate the precise average speed.", "### Step 1: Calculate Total Distance Traveled", "The first step in determining average speed is summing the total distance covered.", "- Distance for the first leg: 150 km\n- Distance for the second leg: 90 km\n- Total Distance = 150 km + 90 km = 240 km", "### Step 2: Calculate Total Travel Time", "Next, add the total time spent on the trip.", "- Time for the first leg: 2 hours\n- Time for the second leg: 1.5 hours\n- Total Time = 2 + 1.5 = 3.5 hours", "### Step 3: Calculate Average Speed", "Average speed is calculated using the formula:", "[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}}\n]", "Plugging in the numbers:", "[\n\ ext{Average Speed} = \frac{240 \ ext{ km}}{3.5 \ ext{ hours}} = 68.57 \ ext{ km/h (approximately)}\n]", "### Final Insight", "The car achieved an average speed of about 68.57 km/h over the entire trip. While this speed doesn’t reflect peak performance during either leg — the first at 75 km/h (150 km ÷ 2 h) and the second slightly faster at 60 km/h (90 km ÷ 1.5 h) — the average accounts for the total distance and combined travel time.", "### Why Average Speed Matters", "Understanding average speed helps drivers and travelers assess journey efficiency beyond simple speed readings. It factors in delays, stops, terrain changes, and traffic, offering a realistic snapshot of overall travel performance. For long-distance trips or planning commutes, knowing average speed aids in better time management and fuel use calculations.", "In summary: A car that travels 150 km in 2 hours and then 90 km in 1.5 hours delivers an average speed of approximately 68.57 km/h, reflecting a balanced and efficient journey across 240 kilometers in 3.5 hours."]
