Metro trains shuttle between Shahdara and Rithala stations at a regular…

Concept: When trains start together from both ends of a route and repeat at a fixed interval, a train that takes T minutes for the one-way journey meets every opposite-end departure whose start time falls within its own travel window (from its own departure instant up to, but not including, the instant it completes the journey). A departure that occurs only after the reference train has already finished its journey never shares the track with it, so it is not met.

Application:

1. Trains run every 4 minutes from both Shahdara and Rithala and take 37 minutes for the one-way journey; the very first departures from both stations occur together at 9:00 am (service starts only from 9:00 am, so no earlier trains exist).

2. The train being tracked departs Rithala at 9:00 am and, taking 37 minutes, arrives at Shahdara at 9:37 am - so it is on the track only from 9:00 am until 9:37 am.

3. A train leaving Shahdara at time t shares the track with this reference train - and therefore crosses it - exactly when 9:00 am is less than or equal to t, and t is less than 9:37 am.

4. Listing the Shahdara departures at the 4-minute spacing inside this window: 9:00 am, 9:04 am, 9:08 am, 9:12 am, 9:16 am, 9:20 am, 9:24 am, 9:28 am, 9:32 am, and 9:36 am.

5. That is ten departures, so ten trains from Shahdara cross the reference Rithala train.

Cross-check: The next Shahdara departure after 9:36 am would be at 9:40 am, but the Rithala train already reaches Shahdara at 9:37 am - three minutes earlier - so that later train never shares the track with it and is correctly left out. This confirms the count stops at 9:36 am and totals exactly ten.