a
Lv 6
a asked in Science & MathematicsMathematics · 1 decade ago

algebra... head and tail wind?

with a head wind a plane traveled 500 miles in 5 hours. with a tail wind the plane flew the return trip in 4 hours and 10 minutes. find the speed of the plane and the speed of the wind

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  • 1 decade ago
    Favorite Answer

    Hi,

    25/6(P + W) = 500

    5(P - W) = 500

    25/6(P + W) = 500

    5P - 5W = 500

    Multiply the first equation by 6 to eliminate the fraction. Multiply the second equation by -5. Add the equations and solve.

    25(P + W) = 3000

    5P - 5W = 500

    25P + 25W = 3000

    -5(5P - 5W = 500)

    25P + 25W = 3000

    -25P + 25W = -2500

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

    50W = 200

    W = 10

    If W = 10 and 5(P - W) = 500, then:

    5(P - 10) = 500

    5P - 50 = 500

    5P = 550

    P = 110

    The plane's speed is 110 mph and the wind's speed is 10mph. <==ANSWER

    I hope that helps!! :-)

  • Joel L
    Lv 6
    1 decade ago

    First trip ground speed was 500 miles / 5 hours = 100 mi/hr

    Return trip ground speed was 500 miles / 4 1/6 hours = 120 mi/hr

    The air speed is 110 mi/hr and the wind speed is 10 mi/hr

  • 1 decade ago

    how would you solve it?

    you have two trips.. each with a speed. If you average the two speeds, you have the speed of the plane, and the difference between the speed of each trip and the plane speed is the wind speed.

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