Originally Posted by
Andy Somnifac
That is where your logic is flawed. You seem to be assuming that because you used an example where it wasn't possible, it must not be possible in all cases. The scenario above shows that not to be the case, and seems to me to be a completely realistic scenario.
What you say is correct in theory. Potential energy is built up going up hills and later released going down.
However ... you can not, by the laws of physics, ever make up the lost speed in climbing by gaining more speed in descending.
Why?
Air resistance is a square function and so it'll increase substantially the faster you go, slowing you down.
This means that if you go 2 hours at 20mph the overall air resistance will be significantly lower than if you would go 1 hour at 10mph followed by 1 hour at 30mph.
In case you didn't know, air resistance is the single most important factor for speed on a bike, dwarving such little factors like rolling resistance or weight.