Joules of energy

Question

In kick boxing, the energy needed to break a board of standard width and thickness varies inversely with the length of the board. If 3.7 Joules of energy are required to break a 30-inch board, how many Joules of energy are required to break a 24-inch board?

Answer 1

They vary inversely. So if we need E joules to break an x-inch board, that means that E=k/x, for some constant k.

You say that we need 3.7 joules to break a 30-inch board. So 3.7=k/30. Multiply both sides by 30 to get 111=k.

 

So the equation becomes E=111/x. For a 24-inch board, this means E=111/24=37/8=4.625 joules of energy.