Answer
$$109m$$
Work Step by Step
Since el-Guerrouj has run the mile in less time than the time Roger takes to run the same distance, el-Guerrouj will win the race. We find:
$$
D=v_{a v g .} t_{G}
$$
Where $v_{a r g}$ is the average velocity for Roger and $t_{G}$ is the time that el-Guerrouj takes to finish the mile; thus:
$$
\frac{(1609 \mathrm{m})}{t_{R}} t_{G}=D
$$
We are told that $t_{G}=3: 43.13=3 \times 60+43.13=223.13 \mathrm{s}$ , $t_{R}=3: 59.4=3 \times 60+59.4=239.4 \mathrm{s},$ so:
$$
\begin{aligned}
&\frac{(1609 \mathrm{m})}{(239.4 \mathrm{s})}(223.13 \mathrm{s})=D \\
&=1500 \mathrm{m}
\end{aligned}
$$
This is the distance that Roger runs when el-Guerrouj runs the mile, thus el-Guerrouj would have won by:
$$
109 \mathrm{m}=(1609 \mathrm{m})-(1500 \mathrm{m})
$$
