In each hour, a train starts from station $A$ to station $B$ and another starts from station $B$ to station $A$. Each train has the same speed and takes $5$ hours to reach the other station. How many trains a train will meet in its way from one station to the other station?
My answer is $11$, but my book says the answer is $10$.
My explanation: Suppose, Train X is starting from station $A$ to station $B$. Train X meets $1$ another train when it starts to leave the station. Then Train X meets with $1$ another train in every $30$ minutes and meets the 11th train when it enters to station $B$.
Could anyone please help me understand what I'm doing wrong.
When not entering or exiting the station 9 are met (on the journey itself) but then an additional two, one at the start as it leaves the station and then one as it arrives as you say... I understand how the answer could be 9 or 11 due to the ambiguity of whether meeting in the station counts but in either case, the answer is not 10. Maybe whoever wrote the answers simply did 5 / (1/2) = 10 rather than consider the meeting at time 0 or 5.