Christie pilots her plane for 320 miles against a headwind in 2 hours. the flight would take 1 hour and 36 minutes with a tailwind of the same speed. find the headwind and the speed of the plane in still air

Let us say that s is the speed of the plane and x is the speed of the headwind so that:

s - x = (320 / 2) = 160

s + x = (320 / 1.6) = 200

So we got two equations:

s - x = 160

s + x = 200

Adding the two equations:

2s = 360

s = 180 mph (speed of plane)

So x is:

x = 180 - 160

x = 20 mph (headwind)