Question

An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

Answer 1

Let the usual speed of aero plane be x km/hr. Then,

Increased speed of the aero plane = (x + 100)km/hr

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

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

Therefore,

`1200/x-1200/(x+100)=1`

`(1200(x+100)-1200x)/(x(x+100x))=1`

`(1200x+120000-1200x)/(x^2+100x)=1`

`12000/(x^2+100x)=1`

120000 = x² + 100x

x² + 100x - 120000 = 0

x² - 300x + 400x - 120000 = 0

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

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

So, either 

x - 300 = 0

x = 300

Or

x + 400 = 0

x = -400

But, the speed of the aero plane can never be negative.

Hence, the usual speed of train is x = 300 km/hr