**Average Speed Calculation:**

To calculate the average speed of the car, we need to consider the total distance traveled and the total time taken.

**Step 1: Calculate the total distance:**

Let's assume the total distance covered by the car is D.

According to the question, the car covers one-third of the distance with a speed of 20 km/h. So, the distance covered at 20 km/h can be calculated as:

Distance1 = (1/3) * D

The remaining distance is covered at a speed of 60 km/h, which can be calculated as:

Distance2 = (2/3) * D

Therefore, the total distance covered is:

Total distance = Distance1 + Distance2 = (1/3) * D + (2/3) * D = D

So, the total distance covered by the car is D.

**Step 2: Calculate the total time taken:**

To find the average speed, we need to calculate the total time taken by the car.

The time taken to cover Distance1 at a speed of 20 km/h can be calculated using the formula:

Time1 = Distance1 / Speed1

Given that Speed1 = 20 km/h and Distance1 = (1/3) * D, we can substitute these values into the formula:

Time1 = [(1/3) * D] / 20

Similarly, the time taken to cover Distance2 at a speed of 60 km/h can be calculated as:

Time2 = Distance2 / Speed2

Given that Speed2 = 60 km/h and Distance2 = (2/3) * D, we can substitute these values into the formula:

Time2 = [(2/3) * D] / 60

Therefore, the total time taken is:

Total time = Time1 + Time2 = [(1/3) * D] / 20 + [(2/3) * D] / 60

**Step 3: Calculate the average speed:**

The average speed can be calculated by dividing the total distance by the total time taken:

Average speed = Total distance / Total time

Substituting the values of the total distance and total time, we get:

Average speed = D / [(1/3) * D / 20 + (2/3) * D / 60]

Simplifying the equation:

Average speed = 1 / [(1/3) / 20 + (2/3) / 60]

Now, let's simplify the expression within the brackets:

Average speed = 1 / (1/60 + 2/180)

Average speed = 1 / (3/180 + 2/180)

Average speed = 1 / (5/180)

Average speed = 180 / 5

Average speed = 36 km/h

Therefore, the average speed of the car is 36 km/h.

36kmph