Originally Posted by plantrob

Except that it's wrong. Or at least overly simplistic. If your power output on a flat is 200W, and you maintain that power output on the uphill as well as on the downhill, your time (and therefore your average velocity) should be identical for the flat and the hill ride (if wind resistance is the same for both rides). Two problems:
* I haven't found a way to put as much power into a downhill stretch as I do uphill (if I did, I would reach a truly neckbreaking speed)
* as mentioned previously in this thread, wind resistance increases more than linearly with velocity - so you're better off riding your steady speed on the flat than the slow - fast up and down the hill.

Both of these effects are more pronounced the steeper the hill is (especially the downhill). So on a two-mile stretch, your average speed should be better if it includes two 50-ft hills than with one 100-ft hill; and it will be better on a ride with 100ft ascent over half a mile followed by 100ft descent over 1.5 miles then on a ride with 100ft ascent on first mile, followed by 100ft descent on second mile.

So there are perfectly good reasons why average speed should be slower on hills, but the middle-school math has very little to do with it.