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

9.6 pounds of pressure

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`