CHSR and Caltrain trains will be sharing tracks over 47 miles between SJ and SF. The CHSR trains will reach maximum speeds of just 110 mph while the Caltrain trains will reach 79 mph, lets say 80 mph to make the following math simpler.
47 miles / 110 mph = 0.427 hours or 25.6 minutes.
47 miles / 80 mph = 0.587 hours or 35.3 minutes.
The CHSR train will make just one intermediate stop, so add 2 minutes or so for 2728 minutes. The Caltrain train will make 19 intermediate stops, so add 38 minutes or so for 73 minutes. It actually takes around 93 minutes or so per the schedule now, because the train does not go 80 mph all the way.
Let's assume CHSR is running trains every half hour over these 47 miles, and Caltrain is running trains every half hour as well. Let's give the Caltrain train a half hour start. In about a half hour it will go around 16 miles (one third 47 miles). That's when CHSR departs 16 miles behind the Caltrain train. In another half hour, the Caltrain goes another 16 miles. In that same second half hour, the CHSR train goes 6/7 of the 47 miles, around 40 miles. It passes the slower Caltrain once. The CHSR train will reach the end of the 47 miles long before the Caltrain train, but it will not pass a second Caltrain train as both should reach the end station at the same time. So only one passing siding is needed under the best of circumstances, i.e. the Caltrain train leaving after the CHSR train, and therefore a half hour before the next CHSR train.
