Agreement on the seesaw

PLAYGROUND NEWS. A goat and a cat reached an agreement on the seesaw today, after a week of arguing.

Goat $G$ and cat $C$ agree on the seesaw after a week of arguing.

Goat $G=30$ and cat $C=5$ kg.

The goat weighs thirty kilograms and the cat five. If both sit at the same distance from the middle, the goat goes down and the cat goes up in the air.

$G=30$ kg and $C=5$ kg. For every distance $d>0$ from the middle, $30d>5d$, so the goat goes down.

$\forall d>0,30d>5d$

The solution was not to change the weights but the places. The goat sat half a metre from the middle and the cat three metres. Thirty times a half is fifteen, and five times three is fifteen too. The seesaw stayed level, and with one sitting at each end the plank was three and a half metres long.

Goat at $0.5$ m and cat at $3$ m: $30\times 0.5=15$ and $5\times 3=15$, so it is level. The plank is $0.5+3=3.5$ m.

$30\times 0.5=5\times 3=15$; plank $0.5+3=3.5$ m

Then the cat moved one metre closer to the middle. Five times two is ten, which is less than fifteen, and the goat's side went down. Balance means weight times distance is the same on both sides.

The cat moved to $2$ m: $5\times 2=10<15$ and the goat's side went down. Level means $G{d}_G=C{d}_C$, with distances $d_G$ and $d_C$.

$5\times 2=10<15$; level means $G{d}_G=C{d}_C$