How many trains are there on the Paris Underground

Hey,

I am new to this too, but I think I have some ideas for your problem.

Your approach looks good, but I think you have a mistake in how you time the trains. You say that there is one train every three stations and that it takes 1m30s to travel the distance from one station to the next. But how long does the train spend at each station?

My approach would be to represent each line as a timeline (the time it would take one train to go from one side to the other). All the trains on the line in a given direction should then be distributed evenly along this timeline in increments of the "average time between trains" + "waiting time at the station" as you already did.

Assumptions:

• 1m 30s travel time between stations
• 1m 00s waiting time per station
• 3m 00s between trains
• 21 Stops per line
• 14 lines

Based on these assumptions we take a total of 2m30s per stop. Now I would also assume that the trains changing direction at the end of the line take the equivalent of one stop to do so, so let's change the average amount of stops per line to 22.

Now the length of our timeline can be calculated as 22stops * 2m30s = 55min.

If there is a train every 3 min we can round the number of trains per leg to 14 (55min/(3min+1min)).

So the total number of trains would now be 14 trains per leg * 2 legs * 14 lines = 392 trains.

Obviously, the assumptions make a major difference, so changing the time between trains to 2min will lead to 504 trains at peak time.

Hope that helps!