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 Kimberley, Ela, and Houston all are sent to collect firewood by their grammy. Kimberley collects ten pounds of firewood, and Houston collects 12 pounds of firewood. If the three of them managed to collect a total of 35 pounds of firewood, how many pounds were collected by Ela? Kimberley and Houston collected 10+12 = <<10+12=22>>22 pounds of firewood. You can find how much Ela collected by subtracting that amount from the total amount collected: 35-22 = <<35-22=13>>13 pounds. #### 13 A new movie gets released and makes $120 million in the box office for its opening weekend. It ends up making 3.5 times that much during its entire run. If the production company gets to keep 60%, how much profit did they make if the movie cost $60 million to produce? Over the movies run it made 120*3.5=<<120*3.5=420>>420 million So the production company made 420,000,000*.6=$<<420000000*.6=252000000>>252,000,000 So they got a profit of 252,000,000-60,000,000=$<<252000000-60000000=192000000>>192,000,000 #### 192000000 Omi is twice as old as Kimiko. Arlette is 3/4 times as old as Kimiko. If Kimiko is 28 years old, calculate the average age of the three? If Kimiko is 28, Omi is 2 * 28 years = <<28*2=56>>56 years old. Arlette is 3/4 * 28 years = <<3/4*28=21>>21 years old. If you add up their ages, it sums to 21 years + 56 years + 28 years = <<21+56+28=105>>105 years The average age for the three is 105 years / 3 people = <<105/3=35>>35 years/person #### 35 A hay farmer harvested 560 bales of hay from 5 acres of grass per month last year. This year, he planted an additional 7 acres of grass. If the farmer also owns 9 horses and each horse consumes 3 bales of hay a day, how many bales of hay would the farmer have left by the end of December if he starts feeding them this year's hay beginning the first day of September? For every acre of grass, the farmer can harvest 560/5 = <<560/5=112>>112 bales of hay each month. This year, the farmer has 7 + 5 = <<7+5=12>>12 acres of grass. He can expect to harvest 12 x 112 = <<12*112=1344>>1344 bales of hay per month. The total hay production this year is 1344*12 = <<1344*12=16128>>16128 From September to December, the farmer would have to feed his horses for a total of 30 + 31 + 30 + 31 = <<30+31+30+31=122>>122 days Each day his horse eats a total of 3*9 = <<3*9=27>>27 bales of hay. For the 122 days, the horses will eat a total of 27*122 = <<27*122=3294>>3294 bales. The total number of bales remaining will be 16128-3294 = <<16128-3294=12834>>12834. #### 12834 A river is to be used for a boat race. If each boat is 3 feet across and they must have at least 2 feet between them or the riverbank, how many boats can race in a river that is 42 feet across? Each boat will require 3 feet across to fit itself and 2 feet space on one side for a total of 2+3 = <<3+2=5>>5 feet per boat The last boat will need an additional 2 feet space on its other side, so this 2 feet should be subtracted first from the 42 feet which leaves 42-2 = <<42-2=40>>40 feet 5 feet per boat on the remaining 40 feet for a total of 40/5 = <<40/5=8>>8 boats #### 8 Joseph and his friends watched two movies in his house. The first movie is 1 hour and 30 minutes long while the second movie is 30 minutes longer than the first. Before the movies, they spent 10 minutes making popcorn and twice as long making fries. How long, in hours, did it take Joseph and his friends to cook and watch the movies? The first movie was 60 + 30 = <<60+30=90>>90 minutes long since an hour has 60 minutes. The second movie was 90 + 30 = <<90+30=120>>120 minutes long. It took them a total of 90 + 120 = <<90+120=210>>210 minutes to watch the two movies. It took them 10 x 2 = <<10*2=20>>20 minutes to cook the fries. Thus, it took them a total of 10 + 20 = <<10+20=30>>30 minutes to cook. So, they spent 210 + 30 = <<210+30=240>>240 minutes watching the movies and cooking. In hours, this is equal to 240/60 = <<240/60=4>>4 hours. #### 4 Eustace is twice as old as Milford. In 3 years, he will be 39. How old will Milford be? Eustace’s current age must be 39 years old – 3 years = <<39-3=36>>36 years old. So Milford’s current age must be 36 years old / 2 = <<36/2=18>>18 years old. So in 3 years, Milford will be 18 years old + 3 years = <<18+3=21>>21 years old. #### 21 Three adults whose average weight is 140 pounds went first in the elevator. Two children whose average weight is 64 pounds also went inside. If an elevator sign reads “Maximum weight 600 pounds.", what is the maximum weight of the next person to get in the elevator so that it will not be overloaded? The sum of the weights of the three adults is 140 x 3 = <<140*3=420>>420 pounds. The sum of the weight of the two children is 64 x 2 = <<64*2=128>>128 pounds. So the total weight of the 5 people who are in the elevator is 420 + 128 = <<420+128=548>>548 pounds. This would mean that the next person's weight must not exceed 600 - 548 = <<600-548=52>>52 pounds. #### 52 Frank needs to meet a quota at work for his sales. It’s the beginning of the month and in 30 days he needs to have 50 cars sold. The first three days he sold 5 cars each day. Then the next 4 days he sold 3 cars each day. If the month is 30 days long how many cars does he need to sell for the remaining days to meet his quota? On days one, two, and three he sold 5 cars each day so, 5 cars + 5 cars + 5 cars = <<5+5+5=15>>15 cars that he sold on those days. On days 4,5,6 and 7 he sold 3 cars each day so, 3 cars + 3 cars + 3 cars + 3 cars = <<3+3+3+3=12>>12 cars that he sold on those days. Now we combine the cars he has already sold, which is 15 cars, and 12 cars, so 15 cars + 12 cars = <<15+12=27>>27 cars are sold in total. If he needs to sell 50 cars and has already sold 27 cars then 50 cars - 27 cars = <<50-27=23>>23 cars left to sell to meet his quota. #### 23