Start the clock when the first train dispatches (that's 1), count as many trains as you want (let's use 6 dispatches as an example), and stop the clock as soon as the 6th train leaves from the station.
(riders/hour)=[(6 trains)-1]*(# of riders per train)*(60 minutes)/(# of minutes between 1st and last dispatch)
or to be more precise:
(riders/hour)=[(6 trains)-1]*(# of riders per train)*(60 minutes per hour)*(60 seconds per minute)/(# of seconds between 1st and last dispatch)
edit: Actually, I think you will have to subtract 1 from the number of trains. It's like how the number of fence posts is 1 more than the number of spaces between them. You're really counting the time until just before the last train leaves, because those riders have not actually gone through the circuit yet. I changed the formula to include this.
I think it might be more intuitive to start the count at 0 and count how many trains have completed the circuit up until just before the last train dispatches, instead of counting the first train and subtracting 1.