A car travels 150 miles in 3 hours, then increases its speed by 20% and travels for another 2 hours. How many total miles does the car travel?
["Title: How Fast Is the Car Traveling? Solving a Real-World Distance Problem", "When analyzing vehicle travel patterns, understanding speed, time, and distance relationships is essential. A practical example involves a car that travels 150 miles in 3 hours, then increases its speed by 20% and continues for another 2 hours. This scenario answers a common question: How many miles does the car travel in total?", "---", "### The First Segment of the Trip", "The car travels 150 miles in 3 hours.\nTo find the speed:", "[\n\ ext{Speed} = \frac{\ ext{Distance}}{\ ext{Time}} = \frac{150 \ ext{ miles}}{3 \ ext{ hours}} = 50 \ ext{ mph}\n]", "---", "### Speed Increase: 20% Faster", "The problem states the car increases its speed by 20% after the first segment.\nTo calculate the new speed:", "[\n\ ext{Increased Speed} = 50 \ ext{ mph} + (20% \ imes 50) = 50 + 10 = 60 \ ext{ mph}\n]", "---", "### Second Segment: 60 mph for 2 Hours", "Now, the car travels at 60 mph for 2 hours. The distance covered in this segment is:", "[\n\ ext{Distance} = \ ext{Speed} \ imes \ ext{Time} = 60 \ ext{ mph} \ imes 2 \ ext{ hours} = 120 \ ext{ miles}\n]", "---", "### Total Distance Traveled", "Add the two segments together:", "[\n150 \ ext{ miles} + 120 \ ext{ miles} = 270 \ ext{ miles}\n]", "---", "Final Answer:\nThe car travels a total of 270 miles.", "---", "## Why This Matters for Drivers and Road Trippers", "Understanding how speed changes affect travel time and distance helps optimize routing, estimate arrival times, and improve fuel efficiency. Knowing that a moderate speed increase of 20% can drastically reduce travel time on longer segments is key in planning efficient journeys.", "---", "### Key Takeaways:", "- Speed = Distance ÷ Time\n- A 20% speed increase from 50 mph results in 60 mph\n- Traveling at 60 mph for 2 hours covers 120 miles\n- Total journey: 150 miles + 120 miles = 270 miles", "Mastering these calculations enhances both personal driving efficiency and automotive analysis in real-world scenarios."]
