#### Answer

$s=\dfrac{3}{4}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use $
t=\dfrac{k}{s}
$ and solve for the value of $k$ with the given $
t
$ and $
s
$ values. Then use the equation of variation to solve for the value of the unknown variable.
$\bf{\text{Solution Details:}}$
Since $t$ varies inversely as $s,$ then $
t=\dfrac{k}{s}
.$ Substituting the given values, $
t=3
$ and $
s=5
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
t=\dfrac{k}{s}
\\\\
3=\dfrac{k}{5}
\\\\
5(3)=\left(\dfrac{k}{5}\right)5
\\\\
15=k
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
t=\dfrac{k}{s}
\\\\
t=\dfrac{15}{s}
.\end{array}
If $t=20,$ then
\begin{array}{l}\require{cancel}
t=\dfrac{15}{s}
\\\\
20=\dfrac{15}{s}
\\\\
s(20)=\left(\dfrac{15}{s}\right)s
\\\\
20s=15
\\\\
s=\dfrac{15}{20}
\\\\
s=\dfrac{\cancel{5}\cdot3}{\cancel{5}\cdot4}
\\\\
s=\dfrac{3}{4}
.\end{array}