A rope overhangs a pulley with a weight on one end and a monkey of the same weight on the other end.
The rope weighs 4ozs per foot and the monkey weighs as many pounds as its mother is years old.

The ages of the monkey and it's mother add up to four years.
The monkeys mother is twice as old as the monkey was when the monkeys mother was half as old as the monkey will be when the monkey is three times as old as the monkeys mother was, when the monkeys mother was three times as old as the monkey.

The weight of the weight and the weight of the rope together are half as much again as the difference between the weight of the rope and the monkey.

How long is the rope?

My brain is smoking...

Ya' lost me at the monkey's mama

I like Pie.

long enough to have a weight on one end go through a pully and have a monkey on the other end..


so Its just the right length.

The monkey is 3 pounds
The monkey mom is 3 years old
The monkey is 1 year old
the rope is 2 feet long.
the weight is 1 pound

let me think on this one!

What he said

Actually I did it wrong. The last sentence wouldn't make sense then.

Imperical units measures messes me up. 1 oz = 1/16 lbs.

So

4ozs = 4/16 or better 1/4 lbs

If the rope hangs on a pulley, that means, the rope's lenght has to be divided by 2 also, because the weight one side and the monkey's weight makes a balance.

so if the rope 4 ozs for one foot, and we assume the monkey's age is not a fractal number but a whole number and the monkey and the mom's age is 4 together, let see.

I assume the monkey mother cannot be the half of the little monkey, so I said the little monkey's age is 1 year old, while the mom is 3 years old. Let's see if it works



the monkey mothers is 3 times as old (3x1).

When she is gonna be 4 years old, the little monkey will be 2yrs old which is twice as old than the mother (4). and when the mother monkey will be 6 years old, the little monkey will be 4, which is twice as old, when the mother was 3x as old (3) when the little monkey was 1.

So my theory worked ,we know the little monkey is 1 year old and the mother is 3 years old.

So I got that one out.




Now to the weight and the rope. ...let's see

In that case, What is the weight of the monkeys uncle minus the pulley?

Actually I did it wrong. The last sentence wouldn't make sense then.

Imperical units measures messes me up. 1 oz = 1/16 lbs.

So

4ozs = 4/16 or better 1/4 lbs

If the rope hangs on a pulley, that means, the rope's lenght has to be divided by 2 also, because the weight one side and the monkey's weight makes a balance.

so if the rope 4 ozs for one foot, and we assume the monkey's age is not a fractal number but a whole number and the monkey and the mom's age is 4 together, let see.

I assume the monkey mother cannot be the half of the little monkey, so I said the little monkey's age is 1 year old, while the mom is 3 years old. Let's see if it works



the monkey mothers is 3 times as old (3x1).

When she is gonna be 4 years old, the little monkey will be 2yrs old which is twice as old than the mother (4). and when the mother monkey will be 6 years old, the little monkey will be 4, which is twice as old, when the mother was 3x as old (3) when the little monkey was 1.

So my theory worked ,we know the little monkey is 1 year old and the mother is 3 years old.

So I got that one out.




Now to the weight and the rope. ...let's see




So now we know, that the little monkey weights as many pounds as its mother years old. so that's easy, 3x1

So the little monkey is 3 lbs.

so we have 3 lbs on one side + rope weight = rope+weight + weight (object)

Rope weight is irrelevant to balance it out, so the weight is 3lbs as well, since it's a balance, so we can say that the weight on the other side is also 3lbs .

The rope's length has to be divided by 2 because if it's a balance, both sides should have the same length - theoretically speaking and assuming the pulley is rollable so it rolls to balance .



(weight of the weight (3 lbs) + x weight for the rope)/2 = x - 3

(3+x)/2 = x-3
3+x = 2x-6
3= x-6
9=x

the rope is 9 lbs so 1 foot is 4 ounces , that means 9 lbs is 144 oz, 144/4 = 36.


The answer is 36 feet the rope is!