Average speed refers to total distance covered divided by the total
time taken.

Here, let the total distnace be x km.

The car covers one third of the total distance that is x/3 km with a speed of 20km/s that is time taken by the car for one third of its journey by the formula distance/speed = (x/3)/20 = x/60 seconds.

Simillary for the rest of its journey (two third of x) its speed was 60km/s.

Time taken = (2x/3)/60 = x/90 seconds.

Therefore total time taken = x/60 + x/90 = x/36 seconds.

Therefore average speed = total distance covered/total time taken = x/(x/36)

= 36 km/sec(answer)

Problem: A car moving on a straight road covers one third of the distance with a speed of 20 km/s and the rest with a speed of 60 km/s. What is the average speed of the car?

Solution:

To find the average speed of the car, we need to first calculate the total distance covered by the car and the total time taken to cover that distance.

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

Calculating the distance:
The car covers one third of the distance at a speed of 20 km/s. This means that the car covers (1/3) * d kilometers at a speed of 20 km/s.
Similarly, the car covers the remaining two-thirds of the distance at a speed of 60 km/s. This means that the car covers (2/3) * d kilometers at a speed of 60 km/s.

Adding these distances together, we get:
Distance covered at 20 km/s = (1/3) * d
Distance covered at 60 km/s = (2/3) * d
Total distance covered = (1/3) * d + (2/3) * d = d

So, the total distance covered by the car is 'd' kilometers.

Calculating the time:
We know that speed is defined as the distance covered per unit time. Therefore, we can calculate the time taken by the car to cover each segment of the distance.

Time taken to cover the first segment (at 20 km/s) = Distance / Speed = (1/3) * d / 20 = (1/60) * d hours.
Time taken to cover the second segment (at 60 km/s) = Distance / Speed = (2/3) * d / 60 = (1/90) * d hours.

Adding these times together, we get:
Total time taken = (1/60) * d + (1/90) * d = (3/180) * d + (2/180) * d = (5/180) * d hours.

Calculating the average speed:
Average speed is defined as the total distance covered divided by the total time taken. Therefore, we can calculate the average speed of the car using the formula:

Average speed = Total distance / Total time = d / ((5/180) * d) = 180/5 = 36 km/s.

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