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Math Help - kinematics challenging question

  1. #1
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    kinematics challenging question

    Dear Sir,

    I need help in the below problem.thanks
    Kingman

    A truck is moving at a uniform speed for 450km. If the average speed is increased by 15 km/h, the journey would have taken 90 minutes less. Find the speed of the truck. ( Ans 60km/h)
    I wonder how this problem can be solved using logical reasoning instead of forming equations and solving them.
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  2. #2
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    Let v be the speed of the truck.
    Time taken by the truck to cover 450 km is
    t = 450/v hr......(1)
    Next new speed is (v + 15).
    Now the time taken by the truck to cover the same distance is
    t - 1.5 = 450/(v + 15).......(2)
    Solve the two equations and find v.
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  3. #3
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    I'm struggling with the concept that "forming equations and solving them" does NOT fall under the heading "logical reasoning".
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  4. #4
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    Thanks for solution but I wonder whether an alternative shorter solution is available ;may be by noticing some important facts or relation and things like ratio or reasoning skill .
    Thanks
    Kingman
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  5. #5
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    Quote Originally Posted by kingman View Post
    Thanks for solution but I wonder whether an alternative shorter solution is available ;may be by noticing some important facts or relation and things like ratio or reasoning skill .
    Thanks
    Kingman
    You can wonder all you want. Post #2 tells you exactly how to do it, there is no simpler alternative. And, to be honest, the solution given to you in post #2 is hardly rocket science mathematics.
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  6. #6
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    Hello, kingman!

    A truck is moving at a uniform speed for 450 km.
    If the average speed is increased by 15 km/h,
    . . the journey would have taken 90 minutes less.
    Find the speed of the truck. ( Ans 60km/h)

    I wonder how this problem can be solved using logical reasoning
    instead of forming equations and solving them.

    I understand your query.
    . . Others assume you are trying to avoid the algebra.

    With many two-vehicle problems, there is a back-door solution
    . . which involves only "logical reasoning". .**

    However, I found no such solution for this problem.

    The best I could do is some intelligent guessing.
    I tried a sequence of speeds and compared their times:

    . . \begin{array}{cc} \text{Speed} & \text{Time} \\ \text{(km/hr)} & \text{(hours)} \\ \hline 15 & 30 \\ 30 & 15 \\ 45 & 10 \\ 60 & \;\;\;7\frac{1}{2}\;* \\ 75 & \;\;\;6\;* \\ 90 & 5  \end{array}

    And I found the two speeds whose times differ by 90 minutes.


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    **

    Example
    Two cars start from the same place.
    Car A drives east at 45 mph.
    Car B drives west at 55 mph.
    When will they be 200 miles apart?

    Back-door Solution
    They are separating at a combined speed of 100 mph.
    It is as if car A is stopped and car B is driving away at 100 mph.
    When will they be 200 miles apart? . . . Two hours.


    Example
    Two cars start from the same place.
    Car A drives east at 45 mph.
    Car B also drives east but at 55 mph.
    When will they be 30 miles apart?

    Back-door Solution
    Car B drives 10 mph faster than Car A.
    It is as if Car A stopped an car B is driving away at 10 mph.
    When will they be 30 miles apart? . . . Three hours.

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  7. #7
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    Thanks Sir for your much awaiting encouragement which is is very helpful for me to move forward. Yes
    you are very insightful and care to understand my need. You see it is the neatness of solution we see beauty in it and not just do it for the sake of getting the answer. this is the real spirit of a good communicator.thanks again good luck
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  8. #8
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    Quote Originally Posted by kingman View Post
    Thanks Sir for your much awaiting encouragement which is is very helpful for me to move forward. Yes
    you are very insightful and care to understand my need. You see it is the neatness of solution we see beauty in it and not just do it for the sake of getting the answer. this is the real spirit of a good communicator.thanks again good luck
    If you want beauty in the solution, clearly say so in your questions. Otherwise people will waste their valuable time giving you a pragmatic solution.
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