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    Topics || Problems

    An airplane, flying with the wind, took 2 hours for a 1000-mile flight, and 2.5 hours for the return flight. Find the wind velocity and the speed of the airplane in still air.
    Solution:

    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 \(50 \text{mph}\)