Calculating Average Speed

To calculate the average speed of a car for the entire journey, we need to consider the distances traveled and the time taken at different speeds. Let's break down the problem into steps:

Step 1: Calculate the distances traveled
- The car travels the first half of the distance at a speed of 30 km/h.
- The second half of the distance is covered at a speed of 50 km/h.

Since the distances are equal, we can assume that the first half is "d" and the second half is also "d".

Step 2: Calculate the time taken for each half of the journey
- The time taken for the first half of the journey can be calculated using the formula: time = distance / speed.
- For the first half, the time taken is d / 30 km/h.
- Similarly, for the second half, the time taken is d / 50 km/h.

Step 3: Calculate the total time taken for the entire journey
- The total time taken is the sum of the time taken for the first and second halves of the journey.

Total time = (d / 30) + (d / 50)

Step 4: Calculate the average speed
- The average speed is calculated by dividing the total distance traveled by the total time taken.

Average speed = Total distance / Total time

Since the total distance is 2d (as both halves are equal), we can substitute it in the average speed formula:

Average speed = 2d / [(d / 30) + (d / 50)]

Simplifying the equation further, we get:

Average speed = 2 / [(1 / 30) + (1 / 50)]

Now, let's calculate the average speed:

Average speed = 2 / [(5/150) + (3/150)] (Converting the fractions to a common denominator)
= 2 / (8/150)
= 2 * (150/8)
= 37.5 km/h

Conclusion:
The average speed of the car for the entire journey is 37.5 km/h.