A cyclist covers his first three km at the speed of 8 km per hour, another two km at 3 km per hour, and the last two km at the speed of 2 km per hour. What is the average speed of that cyclist, commenting on the choice of your average?
Answer (1)
To find the average speed of the cyclist, we need to consider the total distance covered and the total time taken to cover that distance. The average speed is not simply the arithmetic mean of the speeds, because each segment of the trip takes a different amount of time.
Step-by-step Calculation:
Find the time taken for each segment of the trip:
First segment: The cyclist covers 3 km at a speed of 8 km per hour.
Time = Speed Distance = 8 km/h 3 km = 0.375 hours
Second segment: The cyclist covers 2 km at a speed of 3 km per hour.
Time = 3 km/h 2 km ≈ 0.667 hours
Third segment: The cyclist covers 2 km at a speed of 2 km per hour.
Time = 2 km/h 2 km = 1 hour
Calculate the total distance and total time:
Total distance = 3 km + 2 km + 2 km = 7 km
Total time = 0.375 hours + 0.667 hours + 1 hour = 2.042 hours
Calculate the average speed:
The average speed is the total distance divided by the total time.
Average Speed = Total Time Total Distance = 2.042 hours 7 km ≈ 3.43 km/h
Given that the average speed is calculated based on the total time and total distance, it provides a more accurate representation of the cyclist's overall pace across all segments rather than simply averaging the speeds.
