Explanation:

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

Step 1: Calculate the total distance
Let's assume the total distance between the two places is "d" km. Since the car covers the first half of the distance at a speed of 40 km/h, the distance covered in the first half is d/2 km.

Step 2: Calculate the time taken to cover the first half
Using the formula: Time = Distance / Speed, we can calculate the time taken to cover the first half of the distance.
Time taken = (d/2) / 40 = d / 80 hours

Step 3: Calculate the time taken to cover the second half
Similarly, the distance covered in the second half is also d/2 km. The speed during the second half is 60 km/h.
Time taken = (d/2) / 60 = d / 120 hours

Step 4: Calculate the total time taken
The total time taken is the sum of the time taken to cover the first half and the time taken to cover the second half.
Total time = d / 80 + d / 120

Step 5: Calculate the average speed
Now, the average speed can be calculated using the formula: Average Speed = Total Distance / Total Time.

Substituting the values, Average Speed = d / (d / 80 + d / 120)

We can simplify this expression by finding the common denominator and adding the fractions: Average Speed = d * (1/80 + 1/120) / d

Simplifying further, Average Speed = (3d + 2d) / (240d) = 5d / (240d)

Finally, the average speed of the car is 5/240 times the total distance traveled.

Conclusion:
The average speed of the car is 5/240 times the total distance traveled between the two places.