A passenger while boarding the plane, slipped from the stairs and got hurt. The pilot took passenger in the emergency clinic at the airport for treatment. Due to this plane got delayed by half an hour. To reach the destination 1500km away in time so that the passengers could the connecting flight,  the speed of plant was increased by 250km/hr than the usual speed find the usual speed 

Let the usual speed of plane be x km/ hr.

Speed increased by 250 km/hr .

New speed = (x + 250)km/hr

Distance to be covered = 1500 km

Time taken as per usual speed = 1500/x hr

Time taken when speed is increased by 250 km/hr = (1500/x + 250)hr

Acoording to question,

1500/x - 1/2 = 1500/x + 250

1500/x - 1500/x + 250 = 1/2

{1500(x+250) - 1500x}/x(x+250) = 1/2

1500x + 375000 - 1500x = (x²+250x)/2

750000 - x² - 250x = 0

x² + 250x - 750000 = 0

x² + 1000x - 750x - 750000 = 0

x(x+1000) - 750(x+1000) = 0

(x+1000)(x-750) = 0

x = -1000.   x = 750

As speed can not be negative, usual speed of the plane is 750 km/ hr .