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Train Problem

Posted by Math

Two trains start from two different stations A and B. One is going from station A to station B and another from station B to station A. If first train takes 8 hours to complete the journey and the second one takes 12 hours, when do the two trains cross each other?

Answer
The first and second train travel 1/8 and 1/12 respectively of the total distance of AB in one hour . So they cover 1/8 +1/12=5/24 of the distance AB in one hour. That means they will cross each other after 24/5 (4 hours 48 minutes) hours.

 

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4 Comments:

  1. Anonymous said...
    10/27/2006  
    There are two know variables. Distance is applied constant variable because it is the same. And time is given. distance= velocity*time therefore the velocity of the first train is 1/8 distance/hour and for the second 1/12 distance/hour. I'm guessing both trains left the same time. So distance=(1/8+1/12)distance*time. With simplication it will take 4.8 hours.
    Anonymous said...
    10/27/2006  
    There are two know variables. Distance is applied constant variable because it is the same. And time is given. distance= velocity*time therefore the velocity of the first train is 1/8 distance/hour and for the second 1/12 distance/hour. I'm guessing both trains left the same time. So distance=(1/8+1/12)distance*time. With simplication it will take 4.8 hours.
    Unknown said...
    12/07/2007  
    I always got in trouble for over analyzing this problem in school. While above anonymous is correct (as is the 'Answer' given, since .8 hours is exactly 48 minutes) if you assume certain constants, and anonymous touched on one of these, you really don't know that these trains left the station at the same time, and you also don't know that they are traveling a constant speed, when and if they made stops, or, if they did not maintain a constant speed, what their rate of acceleration was nor when or for how long a constant speed was maintained. So if you ever gave the answer 'Not enough information' and it was counted wrong, don't be afraid to back up your answer!
    Math said...
    12/07/2007  
    kristopher,
    This problem is supposed to be for high school students. Since it is not mentioning about a varying speed , acceleration ,etc, etc, we suppose they are constant. I don't think somebody will bother about the stops as well, since it is not mentioned. They will take this only as a matter of a simple problem and use their common sense.

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