so her friend runs 3/5 the distance of Nicole's, and that happens to be 3/8 of a mile.
now, a whole will be 5/5, or 1 whole, and that's how much Nicole runs.
we know that 3/5 of Nicole's distance is 3/8 of a mile, what is 5/5 or 1 whole?
[tex]\bf \begin{array}{ccll}
miles&\stackrel{Nicole's}{distance}\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
\frac{3}{8}&\frac{3}{5}\\\\
m&\frac{5}{5}
\end{array}\implies \cfrac{\quad\frac{3}{8} \quad }{m}=\cfrac{\frac{3}{5}}{\frac{5}{5}}\implies \cfrac{\quad\frac{3}{8} \quad }{\frac{m}{1}}=\cfrac{\frac{3}{5}}{\frac{5}{5}}[/tex]
[tex]\bf \cfrac{3}{8}\cdot \cfrac{1}{m}=\cfrac{3}{5}\cdot \cfrac{5}{5}\implies \cfrac{3}{8m}=\cfrac{3}{5}\implies 15=24m\\\\\\ \cfrac{15}{24}=m\implies \cfrac{5}{8}=m[/tex]
