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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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Solution spoiler | Comment 1 of 7
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 11:00 inclusive i.e. 9: that means 10 trains were seen.

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 13:00 inclusive i.e. 13  that means 14 trains were seen. 

Answer :  1st trav- 10 trains;  2nd trav- 14 trains.++

*+***+***+***+***+***+***+***+***+***+***+***+**

EDIT:
 PLEASE IGNORE THE ABOVE - WRONG HOUR TYPED-REASONING OK, SEE BELOW THE CORECT ANSWERS:

CORRECT ANSWERS:
  1st trav &  2nd trav  -22  trains.++

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.

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. 



Edited on July 12, 2013, 6:25 pm
  Posted by Ady TZIDON on 2013-07-12 11:53:35

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