Sunday 31 August 2014

Taking your mind for a walk on a Sunday Morning

Here is a logico-mathematical puzzle to entertain the idle on a Sunday morning:

A train leaves Moscow at 0800 on the 1st of January, its destination Vladivostok; a distance of is 9289 km. For the first part of the journey, it travels at an average speed of 60km/hr for 18 hours in every 24. The rest of the time it is stationary. The bridge over the Amur River, 8515 km into the journey, has been swept away. Between Krasnoyarsk, 4098 km into the journey and Vladivostok, the train starts to accelerate at a rate of 0.1 m/s2 for one hour in every three while it is moving, until it reaches its maximum velocity of 120kph, at which point it slows back down to 60 kph at the same rate; it then accelerates again.
  1. When will the train arrive at its destination?
  2. If the average speed for 18/24 hours is 70kph for the first part of the journey, when will it arrive?
  3. If the rate of acceleration and deceleration is 0.07 m/s2, how much longer will it take to arrive at its destination?
  4. If the rate of acceleration and deceleration is 0.2 m/s2, how much sooner would the train reach its destination?
  5.  On the same train, 500 passengers start the journey at Moscow. The train picks up new passengers at a rate of 20 per hour. The passengers alight on average at a rate of 18 per hour until Chita, 6199km into the journey, after which time the numbers joining and leaving the train are equal. The rate of acceleration changes by 0.01 m/s2 for every 100 extra/fewer passengers on board. What difference will this make to the total journey time?


Look forward to your answers.

6 comments:

  1. The train arrives after three years, two months, twenty days and five hours, plus or minus 123 days. This can be reduced if the contract to rebuild the bridge is issued to the Vladivostok navy shipyard. I have a good friend who manages their infrastructure department and we can set up a joint stock corporation to do the job. However we need $10 million to pay the fees to the governor, the environmental agency, and the GRU and interior ministry troops who have to let us import 2000 Chinese for the job.

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  2. The train can only reach its destination if the bridge is fixed. Otherwise, all the passengers might die. Given that the gross value of the train and all its passengers is putatively lower than the cost of fixing the bridge, at what point does it become economically no longer viable to save the train?

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  3. When you are sure there won´t be anymore trains trying to cross the bridge. My analysis shows the Russian Federation has a strategic interest in maintaining that rail link because the sea passage on the Northern Sea Route gets choked with ice in the winter. The present value analysis demonstrates the bridge will be replaced by using a much larger and sturdier set of steel girders supplied by the Vladivostok shipyard.

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  4. Fergus, I understand you are in the UK? I was wondering if you could look at my blog and tell me which photograph you see in the blog roll for "Venezuela Falling into moral and economic ruins".

    I inserted a photograph of Nicolas Maduro making his right arm extended with the closed fist salute, which I referred to as "nazi like". However, some friends tell me they don´t see that photograph (neither do I, I´m in Spain).

    I´m also asking anybody who is in the USA to tell me what they see (it will be either a guy with a stiff right arm salute or a bunch of workers on strike).

    I´m starting to think that blogger censors photographs if they "violate european sensitivities". Interestingly, many of us who understand Venezuelan politics think Maduro is a Castro puppet, and Castro seems to be focused on making a rightward turn into fascism.

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    Replies
    1. Fernando, yes the Maduro picture appears first n the article, with the strike pictures following.
      I have seen no evidence of 'censorship' on blogger, but know that a friend in the USA often cannot see the same thing as me; this is normally due to international intellectual property rights.

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  5. I guess they change the photo here in Spain? This is really interesting. In recent days Maduro is making the nazi salute almost all the time. I wonder if he´s too dumb to realize or if he´s doing it on purpose?

    Check this photo from my blog in Spanish

    http://dieta-politica-religion.blogspot.com.es/2014/09/ayudanos-chavez.html

    The photo was placed in an article about Maduro acusing the Catholic Church of being Inquisitors because they complained when Maduro´s party rolled out prayers to Chavez copied from the famous Christian prayer which goes "Our Father who is in heaven....". They changed it to "Chavez in heaven, protect us...etc etc". They seem to be copying the North Koreans.

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What do you think?