Silly question maybe but I have to know - do firm tyres go faster and make it easier to climb?

The problem is, I did my first Time Trial last week around a course of part of my city (beautiful by the way - I get to bike along this piece of scenery - aren't I lucky?! http://rcd.typepad.com/photos/cycle_shots/img_0300.JPG)

Anyway, yeah, I did my first Time Trial last week and I clocked in about 45 minutes 33 seconds. Today, a week later I did my second one, and I clocked in about 40 minutes 25 seconds. It's a good improvement on the surface, but my tyres were pumped up just a few minutes before, which means they would've been more firm than last week. I've been training throughout the week but I'm not sure how much I've improved or if it was just because of the difference in my tyres...lol