Let \(V_w\) be the velocity of the wind, \(V_a\) be the velocity of the airplane in still air.

Velocity \(V\), \(V = \frac{d}{t}\)

Flying with the wind: \(V = V_w + V_a\)

\(\frac{1000}{2} = V_w + V_a\)

\(V_a = \frac{1000}{2} - V_w \)

Flying againts the wind: \(V = -V_w + V_a\)

\(\frac{1000}{2.5} = -V_w + V_a\)

\(V_a = V_w + \frac{1000}{2.5}\)

Equate \(V_a\): \( \frac{1000}{2} - V_w =V_w + \frac{1000}{2.5} \)

\(V_w = 50 \text{mph}\)

\(V_a = 500-50\)

\(V_a = 450 \text{mph}\)

Answer: The velocity of the airplane is \(450 \text{mph}\) and the the velocity of the wind is \(50 \text{mph}\)