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Math Help - grade ten questions?

  1. #1
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    grade ten questions?

    Hi, i was just wondering if anyone could help me out with these two math questions from my homework.

    question 1.) solve the system of equations
    x+3y-z=-14
    7x+6y+z=1
    4x-2y-5z=11

    question 2.)a tain leaves toronto for montreal at the same time as another train leaves montreal for toronto. the cities are 500km apart. The trains pass each other 2 hours later. the train leaving montreal is travelling 50km/h faster than the one leaving from toronto. at what distance away from toronto do the trains pass each other?
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  2. #2
    Senior Member MaxJasper's Avatar
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    Re: grade ten questions?

    1) {x,y,z}={4,-5,3}
    2) 200 km
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: grade ten questions?

    1.) One method we may use is elimination. I would begin by taking the first two equations:

    x+3y-z=-14

    7x+6y+z=1

    Notice if we add the equations together, we will eliminate the z:

    8x+9y=-13

    Next, we could take -5 times the first equation and add it to the third to also eliminate z: Then you will have a 2X2 system in x and y, which you may solve, then you will be able to find z from any of you original equations.

    2.) Let train 1 be the train that departed Toronto, and train 2 be the train that departed Montreal. We will subscript all variables accordingly. We are being asked to find d_1

    After traveling for 2 hours, the trains meet, so we know the sum of their traveled distances is 500 km:

    t_1=t_2=2

    d_1+d_2=500

    We are also told:

    v_2=v_1+50

    The relationship between distance, speed and time is d=vt, so we may state:

    v_1t_1+v_2t_2=500

    Using the above information, you can find the quantity in question.
    Last edited by MarkFL; September 16th 2012 at 02:26 AM.
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  4. #4
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    Re: grade ten questions?

    Quote Originally Posted by njdevils1833 View Post
    a tain leaves toronto for montreal at the same time as another train leaves montreal for toronto. the cities are 500km apart. The trains pass each other 2 hours later. the train leaving montreal is travelling 50km/h faster than the one leaving from toronto. at what distance away from toronto do the trains pass each other?
    Toronto(@v mph).........x miles............>[2 hours]<..............500-x miles.............(@v+50)Montreal
    Use speed = distance / time ; solve for x
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  5. #5
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    Re: grade ten questions?

    Hello, njdevils1833!

    Another approach . . .


    2) A train leaves Toronto for Montreal at the same time as another train leaves Montreal for Toronto.
    The cities are 500km apart. .The trains pass each other 2 hours later.
    The train leaving Montreal is travelling 50km/hr faster than the one leaving from Toronto.
    At what distance away from Toronto do the trains pass each other?

    Let v = speed of the train leaving Toronto.
    Then v+50 = speed of the train leaving Montreal.

    Code:
    
          :   2v    :    2(v+50)    :
          *-------->*<--------------*
          T         X               M
          : - - - - - 500 - - - - - :
    In 2 hours, they meet at X.
    The train from Toronto has traveled 2v km.
    The train from Montreal has traveled 2(v+50) km.

    Together, they covered 500 km: . 2v + 2(v+50) \:=\:500
    . . Hence: . v \,=\,100 km/hr.

    Therefore, X is: 2v = 200 km from Toronto.
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