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How many trains? (Posted on 2013-07-12) Difficulty: 2 of 5
Two travelers set out at the same time to travel opposite ways round a circular railway. Trains start each way every fifteen minutes: on the hour, fifteen minutes past, half past, and forty-five minutes past. Clockwise trains take two hours for the journey, counterclockwise trains take three hours.

Including trains seen at the starting point and the ones they are traveling on, how many trains did each traveler see on his journey?

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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re: solution | Comment 3 of 7 |
(In reply to solution by Charlie)


Both you and I placed erroneous answers .<o:p></o:p>

 I have typed wrong arrival hours and YOU HAVE MISSED ONE TRAIN- EITHER THE ONE THAT arirves as you leave or the one that leaves exactly as you arrive).<o:p></o:p>

Here is the right one (same reasoning , but correct TOA):<o:p></o:p>



  1st trav &  2nd trav  -22  trains.++<o:p></o:p>


Assume that the clockwise train left at 12:00 and finished its round at 14:00 - he met the trains  that left between 9:00 and 14:00 inclusive i.e. 5*4*1=21, SINCE THERE ARE 20 INTERVALS REPRESENTING 21 TRAINS . ADD YOUR OWN  TRAIN - THAT means 22  trains were seen.<o:p></o:p>


Apply the same reasoning to the other train: left at 12:00 and finished its round at 15:00 - he met the trains  that left between 10:00 and 15:00 inclusive i.e. 21   that means 22 trains were seen. <o:p></o:p>




  Posted by Ady TZIDON on 2013-07-12 18:39:04
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