smc

Let the speeds of the runners in miles per hour be $a,b,c$, with $a>b>c$. If person $a$ reaches the finish line in $h$ hours, then we have $10=ah,8=bh,6=bh$. Thus, the speeds of the second and third place people are $\frac{8}{h}$ and $\frac{6}{h}$. The ratio of those speeds is $\frac{\frac{8}{h}}{\frac{6}{h}}=\frac{4}{3}$, meaning person $b$ runs $\frac{4}{3}$ times as fast as person $c$, or conversely that person $c$ is $\frac{3}{4}$ times slower than person $b$. If $c$ runs $0.75$ times as fast as $b$, then when $b$ has finished the race at $10$ miles, $c$ will run $10\cdot 0.75=7.5$ miles. This is a difference of $10-7.5=2.5$ miles, which is answer $\boxed{2\frac{1}{2}}$