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Math Help - Word Problem

  1. #1
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    Word Problem

    Hey all, this question has been bugging me for two days, it feels like i can see the solution but i can't quite put my finger on it.

    1.) A car travels half the distance of a journey at an average speed of 80km/h and half at an average speed of x km/h.

    Define a function, S, which gives the average speed for the total journey as a function of x.

    Thanks in advance.
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by andrew2322 View Post
    Hey all, this question has been bugging me for two days, it feels like i can see the solution but i can't quite put my finger on it.

    1.) A car travels half the distance of a journey at an average speed of 80km/h and half at an average speed of x km/h.

    Define a function, S, which gives the average speed for the total journey as a function of x.

    Thanks in advance.
    Maybe I do not understand you correctly, but if half the journey was at 80 km/h and the other half at x km/h, then wouldn't it simply be:

    S = \frac{80 + x}{2}

    Which if you want to write as a function of x can be written as:

    x = 2S - 80
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  3. #3
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    hey

    hello, that was my initial intention however, it was wrong, wrong and wrong again.

    I've tried so many different ways of working it, its so frustrating!!
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Let the total distance travelled is D

    So time taken while travelling with 80kmph = \frac{D}{160}
    and time taken by travelling with x kmph =  <br />
\frac{D}{2x}<br /> <br />
    Function is given by

     <br />
Avg~ Speed ~=\frac{Total~Distance}{Total ~Time}= \frac{D}{\frac{D}{160} + \frac{D}{2x}} <br />

    Go ahead cancel D and simplify
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  5. #5
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by janvdl View Post
    Maybe I do not understand you correctly, but if half the journey was at 80 km/h and the other half at
    x km/h, then wouldn't it simply be:

    S = \frac{80 + x}{2}
    not true in this case
    It won't be correct
    Never try to average the averages
    Last edited by ADARSH; February 17th 2009 at 08:09 AM. Reason: added explanation
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  6. #6
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    hey

    THATS EXACTLY WHAT I DID! well... several times atleast, then i tried many, MANY different other methods and they were all wrong too.
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  7. #7
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by andrew2322 View Post
    THATS EXACTLY WHAT I DID! well... several times atleast, then i tried many, MANY different other methods and they were all wrong too.
    what's the answer, because either your question is wrong or the answer
    Last edited by ADARSH; February 17th 2009 at 08:16 AM.
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