Age of a worker bee day 1 - to hatching, 20 days
Age of a drone day 1 - to hatching, 24 days
Age of a Queen day 1 to hatching,18 days
Queen Bee Maths is more complex and is dependant on how the colony is managed. A good reckoner covering most eventualities can be found here
Fibonacci and bees
The Fibonacci sequence is 1, 1, 2, 3, 5, 8, . An example is the family tree of bees. In every bee hive there is one female queen bee who lays all the eggs. An unfertilised egg hatches into a drone. A fertilised egg hatches into a female worker bee, who doesn't lay any eggs herself.
A drone bee has one parent (the queen bee) who herself has two parents (since she comes from a fertilised egg). This means that the the drone has two grandparents. One of those will be male and therefore have one parent, while the other being female will have two. The drone now has three great grandparents. One is male and only has one parent, the other two are female and have two parents each. The drone now has five great-great grandparents. Moving up the sequence the drone has eight great-great-great grandparents and thirteen great-great-great-great grandparents . 1, 1, 2, 3, 5, 8, 13. Does it look familiar?
For a full genetic diagram click here.