Question

A plane left 40 minutes late due to bad weather and in order to reach the destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.

Answer 1

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.