In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

Let's denote the original speed as 'x' km/hr. Therefore, the original time taken to cover 600 km would be 600/x hours.

Due to bad weather, the speed was reduced by 200 km/hr, making the new speed x-200 km/hr. This increased the time of flight by 30 minutes, which is 0.5 hours. So, the new time taken to cover 600 km is 600/(x-200) hours.

According to the problem, the new time is 0.5 hours more than the original time. We can write this as:

600/x + 0.5 = 600/(x-200)

To solve for x, we first get rid of the fractions by multiplying the whole equation by x(x-200):

600(x-200) + 0.5x(x-200) = 600x

Expanding and simplifying gives:

600x - 120000 + 0.5x^2 - 100x = 600x

Rearranging terms gives a quadratic equation:

0.5x^2 - 100x + 120000 = 0

Multiplying through by 2 to get rid of the decimal gives:

x^2 - 200x + 240000 = 0

This quadratic equation can be factored to:

(x - 400)(x + 600) = 0

The roots of the equation are x = 400 and x = -600. Since speed cannot be negative, we discard x = -600.

Therefore, the original speed of the plane was 400 km/hr.

The original time taken to cover 600 km is 600/400 = 1.5 hours or 1 hour and 30 minutes.

Due to bad weather, the speed was reduced by 200 km/hr to 200 km/hr, and the time of flight increased by 30 minutes to 2 hours.