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Travelers to the train

Travelers to the train

There is a regular train line that connects my town with the city. Trains leave every 10 minutes from both ends of the route that lasts exactly one hour. The operating hours of the service go from 07:00 in the morning until 21:00 at night, which is the time at which the last train leaves each of the terminal stations.

Today I took the 7:50 train to go to school and the 17:30 train to go home.

How many trains in the opposite direction have I crossed?

Solution

If I take the 7:50 train I will cross with all the trains that have left the city from 7:00 (which will arrive to my town from 8:00) until my arrival at the destination station at 8:50 where I will find a train about to leave. That is to say, I will cross with the one that left at 7:00, the one at 7:10, the one at 7:20, ... until the one I meet when I arrive at the station which is the one at 8:50. In total 12 trains.