Problem:
A car travels the first half of the distance between 2 places at a speed of 40km/hr and the second half at the speed of 60km/hr. Calculate the average speed of the car.

Solution:

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

Step 1: Determine the distance:
Let's assume that the total distance between the two places is 'd' km.

Since the car travels the first half of the distance at a speed of 40km/hr, it covers (1/2)d km in the first half.

Similarly, the car travels the second half of the distance at a speed of 60km/hr, covering the remaining (1/2)d km.

Therefore, the total distance traveled by the car is d km.

Step 2: Determine the time taken:
We know that speed = distance/time.

For the first half of the distance, the speed is 40km/hr. Therefore, the time taken to cover the first half of the distance is given by:
Time taken = distance/speed = (1/2)d / 40 = (1/80)d hours.

Similarly, for the second half of the distance, the speed is 60km/hr. Therefore, the time taken to cover the second half of the distance is given by:
Time taken = distance/speed = (1/2)d / 60 = (1/120)d hours.

The total time taken to cover the entire distance is the sum of the time taken for the first and second halves:
Total time taken = (1/80)d + (1/120)d = (3/240)d + (2/240)d = (5/240)d hours.

Step 3: Calculate the average speed:
The average speed is defined as the total distance traveled divided by the total time taken.

Average speed = total distance / total time taken = d / ((5/240)d) = 240/5 = 48 km/hr.

Therefore, the average speed of the car is 48 km/hr.

Conclusion:
- The average speed of the car traveling the first half of the distance at 40 km/hr and the second half at 60 km/hr is 48 km/hr.
- The average speed is calculated by dividing the total distance traveled by the total time taken.
- The total distance is the sum of the distances covered in the first and second halves.
- The total time taken is the sum of the time taken for the first and second halves.