The book was about a boy scout who gets separated from his leader and survives 9 days in the wilderness. It's based on a true story and I think it takes place in the 1920's. The boy also has a brother in the book.

Donn Fendler - Lost On A Mountain In Maine, by Joseph B. Egan, which has become a Maine children's classic.

Donn Fendler - Wikipedia, the free encyclopedia

Lost On a Mountain in Maine

Amazon: When twelve-year-old Donn Fendler gets tired of waiting for his father and brothers to join him on the summit of Maine's highest peak, he decides to find his own way back to camp. But Donn doesn't count on a fast-moving fog that obscures the path. He doesn't count on falling down an embankment that hides him from sight. And he doesn't count on taking a turn that leaves him alone to wander aimlessly for nearly two weeks in the empty mountain wilderness.