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Thread: NEED HELP with simultaneous equation

  1. #1
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    NEED HELP with simultaneous equation

    Tom rides his bicycle from Town A to Town B at an average speed of 20 km/ h. Julia
    walks from Town B to Town A along the same road at an average speed of 5 km/ h.
    The distance along the road between the two towns is 15 km and they each start off
    at the same time.
    a Write two linear equations to model the two journeys. In each case, relate the
    distance in kilometres from Town A to the time travelled in hours.
    b Solve the equations simultaneously using a graphical method to nd the time at
    which they meet along the road between the two towns.
    c How far has each travelled before they meet?

    This is actually from the standard course but I think there's more activity on maths thread in comparison to the standard thread which is why I'm posting on here.
    So fat my two equations are:
    d=20t (for tom)
    d= 15-5t (for Julia)


    When I solve them simultaneously I am not the getting the right answers and they don't even make sense because my answers say they will meet at 33km or something like that, which obviously can't work if the road is 15km.
    Anyway, appreciate all the help
    HSC 2019

    Mathematics Standard - English Advanced - English Extension - Biology - Spanish Continuers - Business studies

  2. #2
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    Re: NEED HELP with simultaneous equation

    Those equations look right to me. For part b you could use a graphing tool like desmos if you don’t feel like drawing it as they are 2 straight lines, and you just want the point of intersection.

    Algebraically:
    Equate the expressions for d as when they meet they will be the same distance from A:
    20t=15-5t
    25t=15
    t=3/5 of an hour (as we are using speed in kilometres per hour). They will meet after 36 minutes.

    For their distance (point where they meet), substitute this value for time (in hours) back into either equation for d.
    d=20(3/5)=12km. Therefore Tom has travelled 12km and Julia has travelled 3km.

  3. #3
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    Re: NEED HELP with simultaneous equation

    Thanks for your help. I have no idea why I wasn't getting that, seems so simple.
    HSC 2019

    Mathematics Standard - English Advanced - English Extension - Biology - Spanish Continuers - Business studies

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