Problem:
A man covers 1/3 of his journey by cycle at 50km/h, next 1/3 by car at 30km/h and the rest by walking at 7km/h. Find his average speed during the whole journey.

Solution:
To calculate the average speed of the entire journey, we need to use the formula:

Average speed = Total distance / Total time

Let's assume the total distance of the journey is D km.

Covering the first 1/3 of the journey:
The man covers the first 1/3 of the journey by cycle at 50km/h. The distance covered by the cycle in this time is (1/3) x D km. The time taken by the man to cover this distance is:

Time taken = Distance / Speed
= (1/3) x D / 50
= D / 150

Covering the second 1/3 of the journey:
Next, the man covers the second 1/3 of the journey by car at 30km/h. The distance covered by the car in this time is (1/3) x D km. The time taken by the man to cover this distance is:

Time taken = Distance / Speed
= (1/3) x D / 30
= D / 90

Covering the final 1/3 of the journey:
Finally, the man covers the last 1/3 of the journey by walking at 7km/h. The distance covered by the man in this time is (1/3) x D km. The time taken by the man to cover this distance is:

Time taken = Distance / Speed
= (1/3) x D / 7
= D / 21

Total time and distance:
The total time taken by the man to cover the entire journey is the sum of the time taken for each part of the journey. Therefore,

Total time = D/150 + D/90 + D/21
= D(1/150 + 1/90 + 1/21)

The total distance covered by the man is D km.

Average speed:
Now, we can calculate the average speed of the entire journey using the formula:

Average speed = Total distance / Total time
= D / [D(1/150 + 1/90 + 1/21)]
= 19.8 km/h

Therefore, the average speed of the man during the entire journey is 19.8 km/h.