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Home » 6. A plane left minutes late due to bad weather and in order to reach the destination, km away in time, it had to increase its speed by from its usual speed. Find the usual speed of the plane.
6. 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.
CBSE | Class 10 | Maths | Maths | Quadratic Equations | Quadratic Equations | RD Sharma
6. 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.

Solution:                

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=2{{x}^{2}}+800x

2{{x}^{2}}+800x-1920000=0

2[{{x}^{2}}+400x-960000]=0

{{x}^{2}}+400x-96000=0

{{x}^{2}}-800x+1200x-96000=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.

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