Calculating Average Speed for a Combined Bike Ride

Introduction

In this article, we will explore the concept of average speed as it applies to a bicycle ride, using a real-world example to illustrate how to calculate it. Average speed is a crucial metric for understanding the overall efficiency of a journey. In this specific case, we will calculate the average speed for a ride consisting of two segments with different distances and average speeds.

Understanding Average Speed

First, let's clarify the formula for average speed, which is a fundamental concept in physics and everyday life:

Average Speed Total Distance Traveled / Total Time Taken

By applying this formula, we can accurately measure the average speed of a journey regardless of the varying speeds and distances involved.

The Problem: A 20 km Bike Ride

A cyclist covers 20 km at an average speed of 8 km/hr and then travels an additional 45 km at an average speed of 10 km/hr. To determine the cyclist's overall average speed for the entire 65 km journey, we need to calculate the total time taken for each segment and then use the average speed formula.

Calculating Time for Each Segment

For the first segment:

Distance: 20 km

Average speed: 8 km/hr

Time taken: 20 km / 8 km/hr 2.5 hours

For the second segment:

Distance: 45 km

Average speed: 10 km/hr

Time taken: 45 km / 10 km/hr 4.5 hours

The total time taken for the entire journey is:

Total time 2.5 hours (first segment) 4.5 hours (second segment) 7 hours

Calculating the Average Speed

Now, using the formula for average speed:

Average Speed Total distance traveled / Total time taken

Average Speed 65 km / 7 hours

Average Speed ≈ 9.29 km/hr

This calculation confirms that the cyclist's overall average speed for the 65 km journey, considering both segments, is approximately 9.29 km/hr.

Comparing Different Methods of Calculation

Let's also examine an alternative method mentioned in the problem statement to ensure consistency:

Total distance 20 km 45 km 65 km

Total time (20 km / 8 km/hr) (45 km / 10 km/hr) 2.5 hours 4.5 hours 7 hours

Average speed 65 km / 7 hours 9.29 km/hr

As expected, these calculations yield the same result, validating the correctness of both methods.

Conclusion

In summary, the average speed for the combined bike ride of 65 km, considering two segments with different distances and average speeds, is approximately 9.29 km/hr. This calculation emphasizes the importance of understanding the underlying principles of average speed in various real-world scenarios, such as travel and transportation planning.