i didnt understand what u were saying about the 7 am departure . Maybe I am missing something but if both trips are 4 1/2 hoursthe trains should see each other every hour, but its only 4 1/2
Think of it when two trains are level, the next coming in the opposite direction is 1 hour (and will always be 1 hour behind) the one you are level with. If it was stationary it would take you an hour to get there but it is also moving towards you!!!!!!!
These assume uniform speed throughout the journey but that complication is irrelevant in terms of the question as it is irrelevant where they pass as long as each has left the station.
Look again at post 12 and appreciate that each train between these times 8am and 4pm has to pass "your" train.
e.g.
the 0800 train leaving NY arrives 1230 Boston.
meanwhile the 0300 train leaving Boston arrives NY 0730
So, the 0800 train from NY will pass the 0400, 0500, 0600, 0700, 0800, 0900,1000, 1100, and 1200 trains leaving Boston
I checked with an online math tutor website and they all seemed to say the same answer. It should be "5". They explained the same reasoning I had. I am not sure where everyone came up with the "one train leaves at noon and the other leaves at 8:00" thing.
I kept rereading the explanations and no offense, but they still dont make any sense. With a train only going 4 1/2 hours and OF THAT the other train goes out once every hours. Its self-explanatory. should be 5
Your calculation is based on the assumption that there were no earlier trains scheduled - that was the mistake I made myself initially, and I admit I didn't see the error until Ginge pointed it out.
But there would be other trains ALREADY on the line going in the opposite direction, when 'your' train left its station, so they also have to be taken into account and counted.
I thought Ginge explained it very succinctly.