Given:
Force is inversely proportional to the length.
That is,
[tex]\begin{gathered} F\infty\frac{1}{L} \\ F=\frac{k}{L}\ldots\ldots\ldots(1) \end{gathered}[/tex]
If F=50 pounds then L=9 inches.
So,
[tex]\begin{gathered} 50=\frac{k}{9} \\ k=450\ldots\ldots\ldots(2) \end{gathered}[/tex]
Substitute (2) in (1) we get,
[tex]F=\frac{450}{L}[/tex]
To find the length when F=20 pounds
[tex]\begin{gathered} 20=\frac{450}{L} \\ L=\frac{450}{20} \\ L=22.5 \end{gathered}[/tex]
Hence, the answer is 22.50 inches.
