A plane flying against the wind covers the 900-kilometer distance between two aerodromes in 2 hours. The same plane flying with the wind cov

Question

A plane flying against the wind covers the 900-kilometer distance between two aerodromes in 2 hours. The same plane flying with the wind covers the same distance in 1 hour and 48 minutes. If the speed of the wind is constant, what is the speed of the wind?

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Acacia 3 years 2021-09-05T15:56:00+00:00 1 Answers 12 views 0

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  1. Tryphena
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    2021-09-05T15:57:08+00:00
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    Answer:

    The speed of the wind is 25 km/hr.

    Explanation:

    Let us call v_p the speed of the plane and v_w the speed of the wind. When the plane is flying against the wind, it covers the distance of 900-km in 2 hours (120 minutes); therefore;

    (1). v_p - v_w = \dfrac{900km}{120min}

    And when the plane is flying with the wind, it covers the same distance in 1 hour 48 minutes (108 minutes)

    (2). v_p+v_w= \dfrac{900km}{108min}

    From equation (1) we solve for v_p and get:

    v_p = \dfrac{900km}{120min}+v_w,

    and by putting this into equation (2) we get:

    \dfrac{900km}{120min}+v_w+v_w= \dfrac{900km}{108min}

    2v_w= \dfrac{900km}{108min}-\dfrac{900km}{120min}

    2v_w = 8.3km/min - 7.5km/min

    2v_w = 0.83km/min

    v_w = 0.4165km/min

    or in km/hr this is

    \boxed{v_w= 25km/hr }

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