Question

An aeroplane 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.

Answer 1

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 = x² + 100x

x² + 100x – 120000 = 0

x² – 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 aeroplane can never be negative.

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