Flying with wind a plane went 255mph. Flying into the same wind the plane went 183 mph. Find the wind speed and the speed of the plane in still air.

Answer 1

Let w = wind speed; s = speed in still air.

Into the wind is s - w = 183

With the wind is s + w = 255 If you add the equations, the w terms cancels out.

2s = 438 divide by 2 so s = 219 mph (speed in still air)

Can solve for wind speed (s) by substituting into one of the eqns: 219 + w = 255 -> w = 255 - 219 = 36 mph

When you think about it, the speed in still air must be the average or midpoint between the two plane speeds as the wind's effect is equal in both directions.

Answer 2

d=rt

distance = rate of speed times time traveled

w = wind speed, p = plane speed in still air

d=rt

d = (p+w)t = 255t

d = (p-w)t = 183t

add to eliminate one variable

2pt = 255t+183t = 438t

2pt = 438t

divide by 2t to eliminate another variable

p= 438t/2t = 219 mph = plane speed in still air

w = 219- 183 = 36 mph = wind speed