#### Answer

$y=\frac{1}{3}$

#### Work Step by Step

$y$ varies inversely as $x$ therefore $y=\frac{k}{x}$
$y=20$ when $x=\frac{1}{4}$. Substitute these values into $y=\frac{k}{x}$ to obtain:
$\require{cancel}
\\y=\frac{k}{x}
\\20=\frac{k}{\frac{1}{4}}
\\20(\frac{1}{4})=\frac{k}{\frac{1}{4}}\cdot \frac{1}{4}
\\20(\frac{1}{4})=\frac{k}{\cancel{\frac{1}{4}}}\cdot \cancel{\frac{1}{4}}
\\5=k$
Thus, the equation for $y$ is $y=\frac{5}{x}$.
To find the value of $y$ when $x=15$, substitute 15 to x in the equation above to obtain:
$\require{cancel}
\\y=\frac{5}{15}
\\y=\frac{1}{3}$