A force of $55$ pounds stretches a spring $3$ inches. Use Hooke s Law to determine how far a force of $25$ pounds will stretch the spring. Round your answer to two decimal places.

A) $1.36$ inches
B) $2.68$ inches
C) $1.56$ inches
D) $1.68$ inches
E) $1.16$ inches

Hooke's Law states that the force $F$ needed to extend or compress a spring by some distance $x$ is proportional to that distance. That is, $F=kx$ , where $k$ is the spring constant. Given that a force of $55$ pounds stretches the spring $3$ inches, we can find $k=\frac{55}{3}$ . To find how far a force of $25$ pounds will stretch the spring, we solve $25=kx$ for $x$ , giving $x=\frac{25}{k}$ . Substituting the value of $k$ we found, $x=\frac{25}{\frac{55}{3}}=\frac{25\cdot 3}{55}=\frac{75}{55}=\mathrm{1.3636...}$ inches, which rounds to $1.36$ inches.