Meeting the Trains

After the field trip to a science museum, two schoolgirls were riding the light rail train back from the downtown to their home suburb station.

“I notice,“ one of the girls said, “that the incoming trains, coming in the opposite direction, pass us every 5 minutes. What do you think - how many trains arrive in downtown from our suburb in an hour, given equal speeds in both directions?“
“Twelve, of course,“ the other girl replied, “because 60 divided by 5 equals 12.“
The first girl did not agree.

What do you think, is it 12 trains an hour or a different number?

Explanations

If the girls had been on a standing train, the first girl's calculations would have been correct, but their train was moving. It took 5 minutes to meet a second train, but then it took the second train 5 more minutes to reach where the girls met the first train. So the time between trains is 10 minutes, not 5, and only 6 trains per hour arrive in the downtown from girl's suburb.

The solution can be seen in a different way - as is presented in the diagram. Meeting a new train every 5 minutes, means the girls would observe 11 trains, while moving. But of these 11 trains only the first 6 would reach the downtown station by the time the girls' train would travel from downtown to their suburb. The last train to reach the downtown station by the time girls' train reaches the suburb's station is the train they would meet exactly in the midway, i.e. the 6th train in the digram. By the time the 6th train reaches downtown (equaling the girls' train reaches the suburb), the 7th, 8th, 9th, 10th, and 11th trains would still be en route to the downtown.

[After Boris A. Kordemsky. The Moscow Puzzles: 359 mathematical recreations. 1972]

Puzzle Meeting the Trains