Question

An aeroplane left 40 minutes late due to heavy rain and in order to reach its destination 1,600 km away in time it had to increase its speed by 40 km per hour from its original speed find the original speed of the aeroplane

Answer 1

Distance = 1600 km

Let the usual speed be = x km/h

now we know that 

speed = distance /time

time = distance / speed

Usual time = 1600/x

Now due to bad weather the speed is increased b 400 km/ hr

which means new speed = 1600/x+400

Now it's given that the plain left 40 minutes late

which means new time = 1600/x+400 + 2/3 ( 40/60 = 2/3 hours)

1600/x = 1600/x+400 +2/3

1600/x-1600/x+400 = 2/3

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

1600x + 640000-1600x/x²+400x = 2/3

640000 = 2/3(x²+400x)

640000 * 3/2 = x²+400x

960000 = x² +400x

0 = x²+400x-960000

0 = x² +1200x-800x-960000

0 = x( x+ 1200) - 800(x+1200)

0= (x+1200)(x-800)

x= -1200 or x= 800

Speed cannot be negative 
∴ usual speed = 800 km/h

Hope it helps!