Answer
It takes the sprinter $9.85\,\mathrm{s}$ to run $100\,\mathrm{m}$.
Work Step by Step
Conversion - $100\,\mathrm{yd}=91.41\,\mathrm{m}$
Speed of the sprinter,\begin{align*}
s&=\frac{d}{t}=\frac{91.41}{9}\\&=10.16\,\mathrm{m/s}
\end{align*}Now, time taken to run $100\,\mathrm{m}$,
\begin{align*}
t&=\frac{d}{s}=\frac{100}{10.16}\\&=9.85\,\mathrm{s}
\end{align*}