Algebra 1

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When a plane flies into the wind, it can travel 3000mi in 6 hr. When it flies with the wind, it can travel the same distance in 5 hr. Find the rate of the plane in still air and the rate of the wind.

  • Algebra 1 -

    x = Rate without wind
    y = Rate of the wind

    T = D/R

    6 = 3000/(x - y)
    6(x - y) = 3000
    6x - 6y = 3000

    5 = 3000/(x + y)
    5(x + y) = 3000
    5x + 5y = 3000

    Solve simultaneously,
    6x - 6y = 3000
    5x + 5y = 3000

    5 *(6x - 6y = 3000)= 30x - 30y = 15,000
    6 *(5x + 5y = 3000)= 30x + 30y = 18,000

    30x - 30y = 15,000
    30x + 30y = 18,000
    60x = 33,000
    x = 550 rate of the plane in still air

    5x + 5y = 3000
    x = 550
    5(550) + 5y = 3000
    2750 + 5y = 3000
    5y = 250
    y = 50 rate of the wind

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