Given information:
- A lady travels at a speed of 20 km/h.
- She returns at a quicker speed.
- The average speed of the whole journey is 24 km/h.

To find:
- The speed of the return journey.

Explanation:
Let's assume the distance of the journey is 'd' km.

Understanding average speed:
The average speed is the total distance traveled divided by the total time taken. Mathematically, it can be represented as:

Average Speed = Total Distance / Total Time

Calculating the total distance:
In this case, the total distance traveled in the forward journey and the return journey is the same, which is 'd' km.

Total Distance = Distance in Forward Journey + Distance in Return Journey
d = d + d
d = 2d

Calculating the total time:
Let's assume the time taken for the forward journey (t1) and the return journey (t2) are in hours.

Total Time = Time in Forward Journey + Time in Return Journey
Total Time = d / Speed in Forward Journey + d / Speed in Return Journey

Applying the given information:
We know that the average speed of the whole journey is 24 km/h. Therefore, we can write:

24 = (2d) / (d / 20 + d / Speed in Return Journey)

Simplifying the equation:
To simplify the equation, we can take the reciprocal of both sides:

1/24 = (d / Speed in Return Journey) / (d / 20 + d / Speed in Return Journey)

Simplifying the right side:

1/24 = 20 / d + Speed in Return Journey / d
1/24 = (20 + Speed in Return Journey) / d

Cross-multiplying:

d = 24 * (20 + Speed in Return Journey)

Calculating the speed of the return journey:
Now, we can solve the equation to find the speed of the return journey.

d = 24 * (20 + Speed in Return Journey)
d = 480 + 24 * Speed in Return Journey
24 * Speed in Return Journey = d - 480
Speed in Return Journey = (d - 480) / 24

Therefore, the speed of the return journey is (d - 480) / 24 km/h.