A car travels 150 miles at an average speed of 50 mph and then travels another 100 miles at an average speed of 40 mph. What is the car's average speed for the entire trip?
["Title: How to Calculate Average Speed for a Multi-Stage Trip: A 150-Mile to 100-Mile Journey", "Understanding average speed is a fundamental concept in driving and travel planning. Whether you're commuting, road-tripping, or analyzing travel efficiency, knowing how to compute the overall average speed for a journey with varying speeds is essential. In this article, we’ll break down the calculation using a practical example: a car traveling 150 miles at an average speed of 50 mph, then continuing for another 100 miles at 40 mph. By mastering this technique, you’ll gain clarity on trip efficiency and optimize future routes.", "---", "### The Journey Breakdown", "Let’s examine the two segments of the trip:", "1. First Segment:\n - Distance: 150 miles\n - Average Speed: 50 mph", "2. Second Segment:\n - Distance: 100 miles\n - Average Speed: 40 mph", "---", "### Step 1: Calculate Time for Each Segment", "Average speed is defined as total distance divided by total time. To compute the total average speed, we first find how long each leg of the journey took.", "First Segment Time:\n[\n\ ext{Time} = \frac{\ ext{Distance}}{\ ext{Speed}} = \frac{150 \ ext{ miles}}{50 \ ext{ mph}} = 3 \ ext{ hours}\n]", "Second Segment Time:\n[\n\ ext{Time} = \frac{100 \ ext{ miles}}{40 \ ext{ mph}} = 2.5 \ ext{ hours}\n]", "---", "### Step 2: Compute Total Distance and Total Time", "- Total Distance:\n[\n150 \ ext{ miles} + 100 \ ext{ miles} = 250 \ ext{ miles}\n]", "- Total Time:\n[\n3 \ ext{ hours} + 2.5 \ ext{ hours} = 5.5 \ ext{ hours}\n]", "---", "### Step 3: Calculate Overall Average Speed", "Now, use the formula for average speed:", "[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}} = \frac{250 \ ext{ miles}}{5.5 \ ext{ hours}} \approx 45.45 \ ext{ mph}\n]", "---", "### Final Answer", "The car’s average speed for the entire trip — 150 miles at 50 mph followed by 100 miles at 40 mph — is approximately 45.45 miles per hour (mph). This result illustrates that average speed isn’t simply the arithmetic mean of the two speeds but reflects the time spent at each speed.", "---", "### Why This Matters", "This calculation helps drivers estimate travel times more accurately, plan fuel usage, and understand efficiency — especially useful for long-distance trips, logistics, or educational purposes in physics and math. Recognizing how speed varies across a journey enables smarter decision-making on the road.", "---", "### Conclusion", "Understanding average speed enhances travel strategy. By dissecting each segment, as shown in this 250-mile trip, you empower yourself with a clear, data-driven insight. Whether you're preparing for a cross-country drive or multiple vehicles, mastering this calculation ensures smoother, more efficient journeys.", "---", "Keywords: average speed calculation, average speed formula, car trip speed, 150 miles 50 mph 100 miles 40 mph, road trip efficiency, travel planning, speed average, time and distance relationship, driving math."]
