7. An aero plane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed of the plane. Find its usual speed.
7. An aero plane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed of the plane. Find its usual speed.

Solution:                                                           

Let’s consider the usual speed of plane as x km/hr,

Then, the increased speed of the plane is = (x + 100) km/hr

Using, speed = distance/ time

Time taken by the plane under usual speed to cover 1200 km = 1200/x hr

Time taken by the plane under increased speed to cover 1200 km = 1200/(x + 100)hr

Given, that the difference in the times is 1 hour. So, this can be expressed as below:       

120000={{x}^{2}}+100x

{{x}^{2}}+100x-120000=0

{{x}^{2}}-300x+400x-120000=0[by factorisation method]

x(x - 300) + 400(x - 300) = 0

x = 300 or x = - 400 neglected as the speed of the aero plane can never be negative.

Therefore, the usual speed of train is 300 km/hr.