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.