To find out the time it takes for the private bus to cover 100 km, we can use the concept of proportionality.
Given that the bus covers 10 km in half an hour, we can set up the following proportion:
10 km / (1/2 hour) = 100 km / x hours
To solve for x, we can cross-multiply and then divide:
10 km * x hours = 100 km * (1/2 hour)
10x = 50
x = 50 / 10
x = 5
Therefore, the bus would take 5 hours to cover 100 km.