Answer
Intensity at 2.5 meters is $I=90\ \text{milliroentgens}\ \text{per}\ \text{hour}$.
Work Step by Step
According to the provided question $I\propto \frac{1}{{{d}^{2}}}$ which can be written as $I=\frac{k}{{{d}^{2}}}$, where I is intensity of radiation, d is the distance from machine and k is a constant.
Substitute d=3 and $I=62.5$ in the equation $I=\frac{k}{{{d}^{2}}}$
$\begin{align}
& I=\frac{k}{{{d}^{2}}} \\
& 62.5=\frac{k}{{{(3)}^{2}}} \\
& k=62.5{{(3)}^{2}} \\
& k=562.5
\end{align}$
Now substitute $k=562.5$ and $d=2.5$ in $I=\frac{k}{{{d}^{2}}}$,
$\begin{align}
& I=\frac{562.5}{{{(2.5)}^{2}}} \\
& \ \ =\frac{562.5}{6.25} \\
& I=90\ \text{milliroentgens}\ \text{per}\ \text{hour}.
\end{align}$
