A cyclist travels at 15 km/h for 2 hours, then increases speed to 20 km/h for the next 3 hours. What is the average speed for the entire trip?
["Understanding Average Speed: A Cyclist’s Journey at Two Speeds", "When analyzing travel times and speeds, one common question cyclists and fitness enthusiasts ask is: What is the average speed during a trip involving different speeds over various durations? Using a real-world example helps illustrate this important concept in physics and daily driving.", "### The Cyclist’s Journey Breakdown", "In this scenario, a cyclist travels:\n- At 15 km/h for 2 hours\n- Then increases speed to 20 km/h for 3 hours", "To find the average speed for the entire trip, we use the fundamental formula:", "[\n\ ext{Average Speed} = \frac{\ ext{Total Distance}}{\ ext{Total Time}}\n]", "### Step 1: Calculate Distance Covered at Each Speed", "- First Segment:\n Speed = 15 km/h\n Time = 2 hours\n Distance = Speed × Time = 15 km/h × 2 h = 30 km", "- Second Segment:\n Speed = 20 km/h\n Time = 3 hours\n Distance = 20 km/h × 3 h = 60 km", "### Step 2: Total Distance and Total Time", "- Total Distance = 30 km + 60 km = 90 km\n- Total Time = 2 hours + 3 hours = 5 hours", "### Step 3: Compute Average Speed", "[\n\ ext{Average Speed} = \frac{90 \ ext{ km}}{5 \ ext{ h}} = 18 \ ext{ km/h}\n]", "### Why This Matters", "Average speed differs from simply taking the arithmetic mean of the two speeds (which would be 17.5 km/h). The actual average reflects how long each segment took—moving longer at 15 km/h reduces overall average speed.", "This calculation applies not just to cycling, but to any multi-speed journey—commuting, road trips, or delivery routes—where speed varies over time.", "### Conclusion", "For a cyclist who rides at 15 km/h for 2 hours and then 20 km/h for 3 hours, the average speed over the entire trip is 18 km/h. Understanding average speed helps cyclists plan journeys, track fitness progress, and optimize travel efficiency. Whether commuting or training, knowing how speed impacts time and distance supports smarter, safer travel decisions.", "Keywords: average speed, cycling journey, calculate average speed, travel time calculation, average velocity, physics problem, distance and speed, cycling average speed", "Meta Description: Discover how to calculate average speed using a cyclist’s trip—15 km/h for 2 hours plus 20 km/h for 3 hours—resulting in a 18 km/h average speed. Learn with step-by-step formulas and real-world application."]
