6.5 miles each way?
http://www.nps.gov/mora/planyourvisit/upload/Carbon%20River_Mowich%20Area%20Trails-2.pdf
Start from Mowich Lake
http://www.associatedcontent.com/article/375076/mount_rainier_camping_and_hiking_mowich.html
Tolmie Peak Trail 5.6 miles round-trip. 1010' elevation gain. Average hiking time:
3 hours. The trail begins at the last bend in the road on the Mowich Lake Road, 5.5
miles from the park boundary. Please stay on main trail near Eunice Lake to protect
the fragile environment.