A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

• 3 hens
  a hen and a half can lay an egg and a half in a day and a half.
  a hen can lay an egg in a day and a half.
  One egg can be laid in 1.5 days by 1 hen
  12 eggs can be laid in 6 days by 1*12*1.5/6 = 3 hens
• 13 years agoHelpfull: Yes(4) No(4)
• H hens × 6 days × 2/3 eggs per hen·day = 12 eggs
  
  Solving for H, we get:
  H = 12 eggs /(6 days × 2/3 eggs per hen·day) = 12/4 = 3 hens
  
  Therefore, the farmer needs 3 hens to produce 12 eggs in 6 days.
• 12 years agoHelpfull: Yes(2) No(4)
• To solve the problem, we first need to find the rate at which the hens lay eggs. The problem can be represented by the following equation, where RATE is the number of eggs produced per hen·day:
  
  1½ hens × 1½ days × RATE = 1½ eggs
  We convert this to fractions thus:
  3/2 hens × 3/2 days × RATE = 3/2 eggs
  
  Multiplying both sides of the equation by 2/3, we get:
  1 hen × 3/2 days × RATE = 1 egg
  
  Multiplying both sides of the equation again by 2/3 and solving for RATE, we get:
  RATE = 2/3 eggs per hen·day
  
  Now that we know the rate at which hens lay eggs, we can calculate how many hens (H) can produce 12 eggs in six days using the following equation:
  
  H hens × 6 days × 2/3 eggs per hen·day = 12 eggs
  
  Solving for H, we get:
  H = 12 eggs /(6 days × 2/3 eggs per hen·day) = 12/4 = 3 hens
  
  Therefore, the farmer needs 3 hens to produce 12 eggs in 6 days.
• 11 years agoHelpfull: Yes(1) No(0)