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He would have to be at 50,000 feet or more to glide 300 miles.........even with a generous glide slope. Thin air helps but few private planes can achieve any altitude even close to that. 20,000 feet is a lot.
glide ratio for a 172 at 70knots is 1 mile for every 1000 feet on a standard pressure day.
10k agl =10 miles