Let’s assume the usual speed of the plane to be x km/hr,
Then the increased speed of the plane is = (x + 4000) km/hr
Using, speed = distance/ time
Time taken by the plane under usual speed to cover 1600 km = 1600/x hr
Time taken by the plane under increased speed to cover 1600 km = 1600/(x + 400) hr
Given, that the difference in the times is 40mins ⇒ 40/60 hours
This can be expressed as below:
1920000 = 2x2 + 800x
2x2 + 800x – 1920000 = 0
2(x2+ 400x – 960000) = 0
x2 + 400x – 960000 = 0
x2 – 800x + 1200x – 960000 = 0 [by factorisation method]
x(x – 800) + 1200(x – 800) = 0
(x – 800)(x + 1200) = 0
x = 800 or x = -1200 (neglected)
As the speed of the train can never be negative.
Thus, the usual speed of the train is 800 km/hr.