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Average speeds on steep climbs, such as the 2009 July 25, Stage 20 - Mont Ventoux are typically under 20km/h (12.5mph), with lowest speeds over short steep sections (typically over a few hundred meters) recorded as being around 15km/h (just under 10mph). However this was not the steepest climb in the Tour ever and I suspect that speeds of closer to 10km/h (around 6mph) over very short distances of very steep climbs are likely.
This question won't make sense, unless you first define the inclination as the speed will depend on the severity of the climb. It's unlikely to ever be below 10 MPH, and if it's really a "climb" it's probably not over 20 MPH.

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Q: What speed do the Tour de France riders go up the steepest hill?
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