Question

An aeroplane left 40 minutes late due to heavy rain and in order to reach its destination, 1600 km away in time,it had to increase its speed by 400km/hr from its original speed. Find the original speed of the plane

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

Answer 2

the speed will increase 400 km