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Thread: Distance Problem *HELP*

  1. #1
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    Distance Problem *HELP*

    hello everybody wondering if anybody can help me out with this one

    - Mary drove from Amity to Belleville at a speed of 50mph. On the way back she drove 60mph. the total trip took 4 2/3 hours of driving time. what is the distance between the 2 cities?
    D = RxT

    Thanks for the help everybody.
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  2. #2
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    Her total distance travelled is $\displaystyle 2.D$

    Her average speed is $\displaystyle (50+60)/2 = 55$ mph

    The total time is 4 2/3 hours or 4.67 hours

    Therefore using the general formula distance=velocity x time,

    $\displaystyle 2.D = 55$ x $\displaystyle 4.67$

    $\displaystyle D = (55$ x $\displaystyle 4.67)/2$

    $\displaystyle D = 128.43$ miles
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  3. #3
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    Hello, Afterme!

    Mary drove from Amity to Belleville at a speed of 50mph.
    On the way back she drove 60mph.
    The total trip took 4 2/3 hours of driving time.
    What is the distance between the 2 cities?

    $\displaystyle D \:= \:R \times T\quad\Rightarrow\quad T \:=\:\frac{D}{R}$

    Going from A to B, Mary drove $\displaystyle D$ miles at 50 mph.
    .Her time was: .$\displaystyle \frac{D}{50}$ hours.

    Going from B to A, Mary drove $\displaystyle D$ miles at 60 mph.
    . . Her time was: .$\displaystyle \frac{D}{60}$ hours.

    Here total time was: $\displaystyle 4\frac{2}{3}\,=\,\frac{14}{3}$ hours.

    There is our equation! . . . $\displaystyle \frac{D}{50} + \frac{D}{60} \;=\;\frac{14}{3}$


    Got it?

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  4. #4
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    I really appreciate it this guys. Thanks
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  5. #5
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    For some reason, you get a slightly different answer between my way and Soroban's way. I think Soroban's way is correct - does that mean there is a flaw in my logic?


    Just re-did this problem using different numbers with a known distance, and I can confirm that my logic is incorrect. Use Soroban's solution technique.
    Last edited by careri; Feb 12th 2008 at 05:57 PM.
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