Calculating Speed for Achieving an Average Speed of 30 kph Over a 80 km Journey: A Step-by-Step Guide

Understanding how to achieve a specific average speed over a given distance is a fundamental concept in transportation and engineering. In this article, we will explore the process to find the required speed for the second part of a 80 km journey to achieve an average speed of 30 kph.

Understanding the Problem

The first part of the journey involves a motorcycle traveling 40 km at a speed of 20 kph. We need to determine the speed of the motorcycle for the next 40 km such that the overall average speed for the entire 80 km journey is 30 kph. Let's break down the solution step-by-step.

Step-by-Step Solution

1. **Calculate the Total Distance:**

The total distance of the journey is:

Total Distance  40 km   40 km  80 km

2. **Calculate the Required Total Time:**

To achieve an average speed of 30 kph over 80 km, we use the formula for average speed:

Average Speed  Total Distance / Total Time30 kph  80 km / Total TimeTotal Time  80 km / 30 kph  8/3 hours approx; 2.67 hours

3. **Calculate the Time Taken for the First 40 km:**

The time taken to cover the first 40 km at 20 kph is:

Time_1  Distance / Speed  40 km / 20 kph  2 hours

4. **Calculate the Remaining Time for the Next 40 km:**

Now we find the remaining time for the second part of the journey:

Remaining Time  Total Time - Time_1  8/3 hours - 2 hours  8/3 - 6/3  2/3 hours

5. **Calculate the Required Speed for the Next 40 km:**

To find the speed needed to cover the next 40 km in 2/3 hours, we use the formula:

Speed  Distance / Time  40 km / (2/3) hours  40 km * (3/2)  60 kph

Conclusion: The speed of the motorcycle for the next 40 km journey should be 60 kph to achieve an average speed of 30 kph for the entire 80 km journey.

Alternative Approach

Alternatively, we can approach the problem using algebra. Let the speed of the motorcycle for the next 40 km be x km/hr.

T1 40 km / 20 km/hr 2 hours T2 40 km / x km/hr Total Time 2 40/x hours

We know the average speed for the whole journey is 30 kph, so we can set up the equation:

Average Speed  Total Distance / Total Time30  80 / (2   40/x)30(2   40/x)  8060   1200/x  801200/x  2  1200 / 20  60 km/hr

Conclusion: The speed of the motorcycle for the next 40 km journey should be 60 km/hr to achieve an average speed of 30 kph for the entire 80 km journey.

Final Thoughts

Calculating the required speed for achieving a specific average speed over a given distance involves a clear and logical approach. By understanding the relationship between distance, speed, and time, you can easily solve similar problems. Whether you use the step-by-step method or the algebraic approach, the key is to apply the basic formulae correctly.