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11 February, 18:23

A plane travels 800 miles in 5 hours with the wind. it went the same distance in 8 hours when flying aginst the wind. find the rate of the wind

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  1. 11 February, 18:58
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    X = planes speed

    y = wind speed

    x + y = plane with wind

    x-y = plane against wind

    800 = 4 (x+y) 4 hours to travel 800 miles with the wind

    800 = 8 (x-y) 8 hours to travel 800 miles against the wind

    distribute the 2 formulas:

    4x + 4y = 800

    8x - 8y = 800

    multiply 1st equation by 2 (8x + 8y = 1600)

    add the 1st and 2nd equations:

    8x + 8y = 1600

    8x - 8y = 800

    16x = 2400

    divide both sides by 16

    x = 2400 / 16

    x = 150

    use original 1st formula to solve for y (wind speed)

    4x + 4y = 800

    4 (150) + 4y = 800

    600 + 4y = 800

    subtract 600 from each side:

    4y = 200

    divide both sides by 4

    y = 200 / 4

    y = 50

    wind speed = 50 miles per hour
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