Still very cold here but the snow has nearly gone. I only received one correct answer to the Chicken and Egg puzzle and that was from Jacki. Everyone else thought the farmer only needed 2 hens – in fact he needed three. Here is the explanation:
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?
This is a classic problem that many people get wrong because they reason that half of a hen cannot lay an egg, and a hen cannot lay half an egg. However, we can get a satisfactory solution by treating this as a purely mathematical problem where the numbers represent averages.
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.
It is rather like those how long does it take a fill a bath problems!!
Tomorrow I have to accompany John to the Land Rover garage as the back door on his LR is not locking. I will have to go in my car and bring him back. I hope there won’t be any ice about – I am very nervous of ice!
Jackson ha discovered he can eat off his paw and scoops up his biscuits one at a time onto his right paw and eats them off it. Goodness knows why he has started to do this – Slip sits under his cat tree waiting for the ones he drops!
I will start a new contest tomorrow. Got to get on with my new site now!