From Oakley, drive east up the Weber Canyon Road for 4.9 miles. Turn right at a junction. There is a gate here, but it is supposed to be un-locked. There are private property signs as well, but this is a public access road owned by the forest service and maintained with tax money, and is always open to the public. If the gate is locked (seasonal), you can walk through. Drive south up the South Fork Weber Canyon Road. Stay on the main road and follow signs labeled "South Fork". Do not park or camp on the road before the forest service boundary. There is a gate at the National Forest boundary. Beyond the gate, the road deteriorates into a 4wd road. The road will reach a stream crossing and use the stream as a roadbed for a while. Park here as the streambed is very rough and not worth the effort to drive.
From the stream crossing mentioned above, follow the rough 4wd track up the canyon and take a right at a junction after a short distance. There is another junction about .5 miles from the stream crossing. Take the track on the left (south). The trail to the right is the White Pine Creek Trail. Continue on the 4wd track south up the canyon. After .75 mile, the track climbs over a steep limestone ridge and the stream disappears into the ground. After this steep climb, the trail passes through a nice meadow and the stream re-appears. The 4wd track eventually fades in to a trail. The trail itself fades out 2.5 to 3 miles past the junction mentioned earlier. When the trail is lost, stay on the right (west) side of the stream, following game and livestock trails until they also fade away. Route-finding is fairly easy at first along the game trails, but then it becomes a bit more difficult. Contine route-finding up the canyon on either side of the stream. At the major divide in the canyon, head southeast (left) to the head of the basin. To climb Duke Mountain from the head of the basin, head cross-country to the east and ascend to the top of the ridge. One the ridge is reached, head west along the ridge to the summit.
A good pair of boots is needed.
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"In fact, I think you should add your body fat to the rating of the climb, to get a true measure of your inner climber. So climbing a 5.7 with 22% body fat is way harder than climbing a 5.14 with 3% body fat."