35 mph for an average sized rider is going to be upwards of 600 watts. Doable for a minute, sure, maybe even two.. for a very strong rider. Waterrockets could do it probably, but I'm going to go out on a limb and say that is beyond the capabilities of most bikeforums members.
30mph, on the other hand, is much more reasonable...
*holds his hand up*
Discount the fact that this happened once with a 40mph tailwind.