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Math Help - A famous question with in-built error

  1. #1
    Junior Member SPOCK's Avatar
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    A famous question with in-built error

    This is a very famous question and most of the members are aware of this question. But this question has an error.

    A train enters into a tunnel AB at A and exits at B. A jackal is sitting at O in another by passing tunnel AOB, which is connected to AB at A and B, where OA is perpendicular to OB. A cat is sitting at P inside the tunnel AB making the shortest possible distance between O and P, such that AO:PB = 30:32. When a train before entering into the tunnel AB makes a whistle (or siren) somewhere before A, the jackal and cat run towards A, they meet with accident (with the train) at the entrance A. Further if the CAT moves towards B instead of A it again meets with accident at the exit of the tunnel by the same train coming from the same direction.

    (This problem has 4 questions attached to it, I am writing only question 2)

    2) The ratio of speeds of jackal is to train is ?


    We have deliberated much on this question and feel that the cat is wrongly typed in the text, which I have highlighted in the text in red and capital letters. We feel that it should be jackal instead of cat. Since the cat will never reach exit B and meet the train at B . Instead the cat will meet the train somewhere before B. Also the question (2) above assumes that the jackal will meet the train at exit B, which is no-where mentioned in the question.

    So my question is whether it will be jackal or cat in the highlighted text. Please give advice and suggestions taking into account the context mentioned above. Please give explanations.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: A famous question with in-built error

    From the info you've provided it's impossible to guess whether the question should be about the cat or the jackal. I can find all the relevant dimensions needed, such as lengths of AP, OP and OB, and from that can get the ratio V_c:V_j (where V_c = velocity of cat and V_j = velocity of jackal). Finally, I can determine the distance prior to A that the train sounds its whistle, so would have no problem answering either question - the ratio of V_c:V_t or V_j:V_t
    Last edited by ebaines; August 4th 2014 at 06:40 AM.
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    Junior Member SPOCK's Avatar
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    Re: A famous question with in-built error

    The answer given to the above question is 1:5 i.e the ratio of speeds of jackal to train is 1:5. But is it ever possible that the cat will meet the train at exit B as given in the text. Also, to answer the question above the answer uses the following equation:
    x/30=(x+50)/40 to determine the value of x which is the distance of the train from the tunnel. The 40 in the denominator suggests that the jackal will meet the train at exit B , which is no-where mentioned in the text. Unless we replace jackal in place of cat highlighted in the text. So my question is how can we assume that the jackal will meet the train at exit B unless specifically mentioned ? And how is it possible that the train meets cat at exit B as mentioned in the text of the problem ? I have tried all the ratios, but the cat will never meet train at exit B. So I think there is an error in the text of the problem. Or, maybe I'm missing something.
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    MHF Contributor ebaines's Avatar
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    Re: A famous question with in-built error

    That equation does indeed solve the problem assuming it's the jackal that meets the train at B instead of the cat. So it seems that there was a typo in the wording of the question. The solution to the problem as worded is x/18 = (x+50)/32, for x = 900/14, and v_j/v_t = 30/(900/14) = 14/30.
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    Junior Member SPOCK's Avatar
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    Re: A famous question with in-built error

    Quote Originally Posted by ebaines View Post
    That equation does indeed solve the problem assuming it's the jackal that meets the train at B instead of the cat. So it seems that there was a typo in the wording of the question. The solution to the problem as worded is x/18 = (x+50)/32, for x = 900/14, and v_j/v_t = 30/(900/14) = 14/30.
    Thanks ! and hence your ratio doesn't match the actual answer 1:5. Because your answer follows the error given in the text that the cat will meet the train at exit B.

    There is one more question in this problem set which involves the speed of cat:-

    What is the ratio of speeds of jackal and cat ? The answer is 5:3. So even if we take this ratio we can find that the cat will never meet the train at exit B. This also proves that there will be jackal in place of cat in the highlighted text. Please inform if you think otherwise.
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