Let total distance covered by body = 3X
Time taken in 1st part which is covered by at a speed 3m/s = X/3
Time taken in 2nd part covered at speed of 6m/s = X/6
Time taken in 3rd part covered at speed of 9m/s = X/9
So, total time taken =( X/3) + (X/6) + (X/9) = 11X/18
Now, average speed of body =( Total distance ) / (Total time)
equal to (54/11) m/s....ans...

$$Hope it's help... $$

Problem Statement: A body covers the first 1/3rd of the total distance with speed 3m/s, the next 1/3rd of the total distance with speed 6m/s, and the last 1/3rd of the total distance with speed 9m/s. Find the average speed of the body.

Solution:
To find the average speed of the body, we need to use the formula:

Average Speed = Total Distance / Total Time

Step 1: Calculate the distance covered in each part

Let's assume that the total distance covered by the body is 'd' meters. Then, the distance covered by the body in each part is:

- Distance covered in the first 1/3rd of the total distance = d/3 meters
- Distance covered in the next 1/3rd of the total distance = d/3 meters
- Distance covered in the last 1/3rd of the total distance = d/3 meters

Step 2: Calculate the time taken to cover each part

We know that:

Time = Distance / Speed

Using this formula, we can calculate the time taken by the body to cover each part:

- Time taken to cover the first 1/3rd of the total distance = (d/3) / 3 m/s = d/9 seconds
- Time taken to cover the next 1/3rd of the total distance = (d/3) / 6 m/s = d/18 seconds
- Time taken to cover the last 1/3rd of the total distance = (d/3) / 9 m/s = d/27 seconds

Step 3: Calculate the total time taken

The total time taken by the body to cover the entire distance is:

Total Time = (d/9) + (d/18) + (d/27) = (3d + 2d + 2d) / 54 = 7d / 54 seconds

Step 4: Find the average speed

Using the formula for average speed, we have:

Average Speed = Total Distance / Total Time
Average Speed = d / (7d/54) = 54/7 m/s

Therefore, the average speed of the body is approximately 7.71 m/s (rounded off to two decimal places).

Conclusion: The average speed of the body is 7.71 m/s.