Question

The force, F, needed to break a board varies inversely with the length, L, of the board. If it takes 24 pounds of pressure to break a board that is 2 feet long, how many pounds of pressure would it take to break a board that is 5 feet long?

Answer 1

Answer:

9.6 pounds of pressure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form $y*x=k$ or $y=k/x$

so

In this problem

$F*L=k$

step 1

Find the value of k

For $F=24\ lb, L=2\ ft$

substitute

$k=(24)(2)=48$

The equation is equal to

$F*L=48$

step 2

For $L=5\ ft$

Find the value of F

substitute the value of L in the equation

$F*(5)=48$

$F=48/5=9.6\ lb$