Question

If the speed of an aeroplane is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the aeroplane.

Answer 1

Let the actual speed of the aeroplane be 'x' km/hr

Speed after reduction = (x - 40) km/hr

Let the actual time taken by the aeroplane be 'y' hrs

The time taken after the speed reduction = y + 20 min

= (y + 20/60) hr {1 min = 1/60 hr}

= (y + 1/3) hr

Total distance = 1200 km

Distance = speed × time

1200 = xy

y = 1200/x -------(1)

After reduction of speed,

1200 = (x - 40) (y + 1/3)

1200 = (x - 40) (3y + 1/3)

1200*3 = (x -40) (3y + 1)

Substitute y = 1200/x,

3600 = (x - 40) (3×1200/x + 1)

3600 = (x - 40) (3600/x + 1)

3600x = (x - 40) (3600 + x)

3600x = x² + 3600x - 40x - 144000

x² - 40x - 144000 = 0

x² - 400x +360x - 144000 = 0

x(x - 400) + 360 (x - 400) = 0

(x - 400) (x + 360)

x-400 = 0 and x+360 = 0

x = 400 and x = -360

As speed can't be negative, we take x value as positive.

i.e., x = 400 km/hr

y = 1200/x

→ y = 1200/400

→ y = 3 hrs

Speed of the aeroplane = 400 km/hr

Actual time taken by the aeroplane = 3 hrs

Hope it helps