Karen is packing her backpack for a long-distance hike. She packs 20 pounds of water, 10 pounds of food, and 20 pounds of gear. During her hike, she drinks 2 pounds of water per hour and eats 1/3rd the weight of food per hour as water per hour. How much weight is she carrying after six hours?
First find the weight of food Karen eats every hour: 2 pounds * 1/3 = 2/3 pounds food.
Then find the total amount of weight Karen's backpack loses per hour she hikes: 2 pounds water/hour + 2/3 pound food/hour = 8/3 pounds/hour.
Multiply this by the number of hours she hikes to find the total amount of weight she loses: 8/3 pounds/hour * 6 hours = <<8/3*6=16>>16 pounds.
Add the weight of all her items to find total starting weight: 20 pounds + 10 pounds + 20 pounds = <<20+10+20=50>>50 pounds.
Then subtract the weight she loses from the starting weight to find the weight after 6 hours: 50 pounds - 16 pounds = <<50-16=34>>34 pounds
#### 34