Question

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

Answer 1

Let the usual speed of the plane be x km/h.

Distance = 1600 km

Usual time = `1600/x` hours

Increased speed = x + 400 km/h

New time = `1600/(x+400)` hours

Given:

The plane left 40 minutes late = `2/3` hour, but still reached on time.

So, the new time is less by `2/3` hour

`1600/x - 1600/(x+400) = 2/3`

ake LCM x(x + 400):

`(1600 xx 400)/(x (x+400)) = 2/3`

`640000/(x(x+400)) = 2/3`

3 × 640000 = 2x(x + 400)

1,920,000 = 2x² + 800x

x² + 400x − 960,000 = 0

(x − 800) (x + 1200) = 0

x = 800 or x = −1200

The usual speed of the plane is: 800 km/h​