Question 188935
Let x=speed of the plane in still air
    y=speed of the head wind
    distance=speed * time

Against the head wind, the speed of the plane is x-y:

(x-y)*2=600          (1)

With the wind, the speed of the plane is x+y:

(x+y)*(5/3)=600      (2)

Simplifying (1) and (2) we get:

2x-2y=600            (1)
(5/3)x+(5/3)y=600    (2)

Equating (1) and (2)

2x-2y=(5/3)x+(5/3)y

Multiply both sides by 3

(2x-2y)*3=((5/3)x+(5/3)y)*3

6x-6y=5x+5y

Solving for x we get:

x=11y         (3)

Substituting 11y for x in (1) we get:


((11y)-y)*2=600
10y*2=600
20y=600
y=30

Solving for x using (3)

x=11(30)
x=330

The speed of the plane in still air is 330kph