Denise has 6 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 9 mph and walks back at a speed of 3 mph, how long should she plan to spend walking back?
Denise spends half of her training time running at 9 mph, so she spends 6 / 2 = <<6/2=3>>3 hours running.
If she runs at 9 mph for 3 hours, she will cover a distance of 9 * 3 = <<9*3=27>>27 miles.
To walk back this distance at 3 mph, Denise will need 27 / 3 = <<27/3=9>>9 hours. Answer: \boxed{9}.