Anonymous
Anonymous asked in Science & MathematicsMathematics · 12 months ago

Write a system of two equations in two variables to solve the problem?

How do I solve this world problem?

Write a system of two equations in two variables to solve the problem.

Flying with a tailwind, a pilot flew an airplane 560 miles in 3.5 hours. Flying into a headwind, the return trip took 4 hours. Find the speed of the plane in calm air and the speed of the wind.

speed in calm air mph:

speed of wind mph:

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  • 12 months ago
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    Recall: s = d/t → where s is the speed, d is the distance, t is the time

    s₁: speed of the plane in calm air

    s₂: speed of wind

    Flying with a tailwind, a pilot flew an airplane 560 miles in 3.5 hours. You can add the 2 speeds together.

    s = s₁ + s₂ = d/t

    s₁ + s₂ = d/t → where: d = 560 miles

    s₁ + s₂ = 560/t → where: t = 3.5 hours

    s₁ + s₂ = 560/3.5

    s₁ + s₂ = 160 ← equation (1)

    Flying into a headwind, the return trip took 4 hours. You must subtract the 2 speeds.

    s = s₁ - s₂ = d/t

    s₁ - s₂ = d/t → where: d = 560 miles

    s₁ - s₂ = 560/t → where: t = 4 hours

    s₁ - s₂ = 560/4

    s₁ - s₂ = 140 ← equation (2)

    You calculate (1) + (2)

    (s₁ + s₂) + (s₁ - s₂) = 160 + 140

    s₁ + s₂ + s₁ - s₂ = 300

    2.s₁ = 300

    s₁ = 150 mph ← speed of the plane

    Recall (2)

    s₁ - s₂ = 140

    s₂ = s₁ - 140 → we've just seen that: s₁ = 150

    s₂ = 10 mph ← speed of the wind

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  • 12 months ago

    Flying with a tailwind, a pilot flew an airplane 560 miles in 3.5 hours.

    Flying into a headwind, the return trip took 4 hours.

    Find the speed of the plane in calm air and the speed of the wind.

    With Wind:

    distance = 560 miles ; time = 3.5 hrs ; rate = 560/3.5 = 160 mph

    -------------------------

    Against Wind:

    distance = 560 miles ; time = 4 hrs ; rate = 140 mph

    ---------------------------

    p + w =160

    p - w = 140

    -----------------

    2p = 300

    p = 150 mph (speed of the plane in still air)

    -----

    Since p + w = 160, w = 10 mph (speed of the wind)

    speed in calm air = 150 mph:

    speed of wind = 10 mph:

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  • 12 months ago

    560/3.5=160 m/h

    560/4= 140 m/h

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  • alex
    Lv 7
    12 months ago

    speed in calm air mph=a

    speed of wind mph= w

    3.5(a+w)=560

    4(a-w)=560

    solve for a , w

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