Question

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

Answer 1

Solution:-
Let the actual speed of the aeroplane be 'x' km/hr
So, speed after reduction = (x - 40) km/hr
Let the actual time taken by the aeroplane be y hr
and the time taken after the speed reduction = y + 20 min = (y + 20/60)
= (y + 1/3) hr
Total distance = 1200 km
So,
Distance = speed$\times$time
1200 = x$\times$y
xy = 1200 .............(1)
After speed reduction,
1200 = (x - 40) (y + 1/3)
1200 = (x - 40) ((3y + 1)/3)
1200$\times$3 = (x -40) (3y + 1)
Now, substituting the value of y from xy= 1200, we get
3600 = (x - 40) ((3$\times$1200)/x + 1)
3600 = (x - 40) (3600/x + 1)

3600

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 and x = -360
Speed can't be negative, so the actual speed of the aeroplane is 400 km/hr
substituting the value of y = 1200/x.
y = 1200/400
y = 3 hours
So, the actual time taken by the aeroplane is 3 hours.
Answer.