Question

In kickboxing, it is found that the pressure, p, needed to break a board varies inversely with the length of the board.If it takes 5 lbs of pressure to break a board that is 2 feet long, how long is the board that requires 18 lbs of pressureto break?

Answer 1

The pressure, p, needed to break a board varies inversely with the length of the board.

Formula for a inverse variation:

$y=\frac{k}{x}$

In the given situation the variable p is the dependent variable (y) and the variable l (length) is the independt variable (x).

Use the given data to find the value of the constant k:

$k=y\cdot x$

if it takes 5 lbs of pressure to break a board that is 2 feet long:

$\begin{gathered} k=5\cdot2 \\ k=10 \end{gathered}$

Using the value of k you get the next equation for the given varation:

$p=\frac{10}{l}$

How long is the board that requires 18 lbs of pressure to break?

Find l when p is 18:

$18=\frac{10}{l}$

solve l:

$\begin{gathered} 18\cdot l=10 \\ l=\frac{10}{18} \\ \\ l=0.55 \end{gathered}$Then, the board that requires 18lbs of pressure to break has a length of 0.55 feet