SOLUTION: Trains on the Glasgow Subway depart every 4 minutes, and a complete circuit takes 24 minutes. Ewan sets off at 8.30 am on a train round in one direction at the same time as another

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Question 1108213: Trains on the Glasgow Subway depart every 4 minutes, and a complete circuit takes 24 minutes. Ewan sets off at 8.30 am on a train round in one direction at the same time as another train leaves in the opposite direction. How many trains will he pass on a complete circuit back to his starting station? (Do not count trains at the start or end station.)
My thoughts:
I was thinking that Ewan is on the train for 24 minutes, so 24/4=6, meaning he stops at 6 stops. Since buses leave every 4 minutes, he encounters 6 buses. This is supposed to be a challenging question, so am I missing something?
Thank you in advance! Your help is much appreciated!
Answer by ikleyn(52767)   (Show Source): You can put this solution on YOUR website!
.
You correctly counted those trains that started at or after 8:30 am in the opposite direction.

There are 6 of them that started at 8:30 am, 8:34 am, 8:38 am, 8:42 am, 8:46 am and 8:50 am.


But you missed to count those trains that started before 8:30 in the opposite direction and arrived to the starting/ending station after 8:30 am.


Ewan will meet those trains too.    (Accounting for these trains and not missing them is the major point of the solution to this problem !)


These are the trains that 

started at 8:06 am     arrived at 8:30 am     (should not be counted)

           8:10 am                8:34 am     (counts)

           8:14 am                8:38 am     (counts)

           8:18 am                8:42 am     (counts)

           8:22 am                8:46 am     (counts)

           8:24 am                8:50 am     (counts)


The number of such trains is  5.


So, the total is  6 + 5 = 11, and I do not count the trains at the start or end station, as the condition requires.


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