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30 May, 16:57

Flying against the wind, an airplane travels 3850 km in 7 hours. Flying with the wind, the same plane travels 4350 km in 5 hours. What is the rate of the plane in still air and what is the rate of the wind?

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  1. 30 May, 17:07
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    The rate of the plane in still air is 710 km/hr and the rate of the wind is 160 km/hr

    Explanation:

    Let Va = the velocity of the airplane

    Let Vw = the velocity of the wind

    When flying with the wind:

    (Va+Vw) * (5 hours) = 4350

    5Va + 5Vw = 4350

    5Vw = 4350 - 5Va

    Vw = 870 - Va

    When flying against the wind:

    (Va-Vw) * (7 hours) = 4200 km

    7Va - 7Vw = 4200

    Substitute 870-Va for Vw and solve for Va:

    7Va - 7 (870-Va) = 3850

    7Va - 6090 + 7Va = 3850

    14Va = 9940

    Va = 710 km/hr

    Rate of wind:

    Vw = 870 - Va

    = 870 - 710

    = 160 km/hour

    Therefore, the rate of the plane in still air is 710 km/hr and the rate of the wind is 160 km/hr
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