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 .
Written on Feb. 28, 2017, 9:21 a.m.