In a flight of 6000 km, an aircraft was slowed down due to bad weather. The average speed for the trip was reduced by 400 kmph and the time of flight increased by 30 minutes. The original planned duration of the flight was :

Let the original planned duration of the flight be x hours
Then,
$$\eqalign{ & \Leftrightarrow \frac{{6000}}{x} - \frac{{600}}{{\left( {x + \frac{1}{2}} \right)}} = 400 \cr & \Leftrightarrow \frac{{6000}}{x} - \frac{{12000}}{{\left( {2x + 1} \right)}} = 400 \cr & \Leftrightarrow \frac{{15}}{x} - \frac{{30}}{{\left( {2x + 1} \right)}} = 1 \cr & \Leftrightarrow 2{x^2} + x - 15 = 0 \cr & \Leftrightarrow \left( {x + 3} \right)\left( {2x - 5} \right) = 0 \cr & \Leftrightarrow x = \frac{5}{2} \cr & \Leftrightarrow x = 2\frac{1}{2} \cr} $$