Think of waiting in line for an amusement park ride. If the ride runs 4 minutes, you'll have to wait in line longer than if ir runs 3 minutes. Same thing, if the guy in the office will leave after 30 years instead of 40 the line waiting or it will move much faster.
And don't feel dumb. We all get hit with it at times ;-)
I feel dumb right now that it wasn’t obvious to me. I was thinking in terms of throughput vs latency, and how for a single pipe, increasing latency doesn’t affect throughput. So why would it change for multiple pipes? My bad intuition was that letting people stay longer would drop throughput until everyone that was in the pipe during the latency change retired, and then throughput would restore to the same as before.
Doing the arithmetic, it’s easy to see why you’re right, but because it wasn’t obvious to me, I’m not surprised it wasn’t obvious to others. Or at least it makes me feel better...