Let the usual speed be x km/hr.
Then, the speed taken = (x + 100) km/hr
Distance = 1500 km
Usual time = distance / usual speed = 1500/x hrs
Time taken = 1500/(x + 100) hrs
It is given that
Time taken = Usual time - 0.5 hrs
=> 1500/x - 1500/(x + 100) = 0.5
=> 1500(x + 100) - 1500x = 0.5x(x + 100)
=> 1500x + 150000 - 1500x = 0.5x² + 50x
=> 0.5x² + 50x - 150000 = 0
=> x² + 100x - 300000 = 0
=> x = (-100 ± √(100² + 4 * 300000))/2
=> x = (-100 ± √1210000)/2
=> x = (-100 ± 1100)/2
=> x = 500 or x = -600
Since speed cannot be negative, x = 500 km/hr
Therefore, the usual speed of the plane is 500 km/hr.