Question

Farmer John has 51 hens. If he had three more solid colored hens, then exactly one-third of his hens would be speckled. From years of experience, Farmer John knows that one-half of the speckled hens will lay speckled eggs and that each hen and a half will lay an egg and a half in a day and a half. After how many full days will Farmer John have 15 dozen speckled eggs to sell?

Answer 1

After full 30 days John will have 15 dozen speckled eggs to sell.

Step-by-step explanation:

Total number of hens John has  = 51 hens

If there are 3 more hens, then total number of hens  = 51 + 3  = 54 hens

Now, one third of the hens are speckled.

$(\frac{1}{3}) \times 54 = 18$  

⇒ 18 hens are speckled.

Now, $(\frac{1}{2})$ of the  total 18 speckled hens  lay speckled eggs.

⇒ 9 hens produce speckled eggs.

Now, one hen lays one egg in a day and a half.

⇒  9  hens lay nine eggs in a day and a half .

⇒  9 hens lay  180 (15 doz.) eggs in $\frac{3}{2} \times\frac{180}{9} = 30$ days

Hence,  after full 30 days John will have 15 dozen speckled eggs to sell.