Question

Nicole's friend runs 3/8 of a mile,but her distance is only 3/5 of Nicole's distance. How far dose Nicole run?

Answer 1

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?


`\bf \begin{array}{ccll} miles&\stackrel{Nicole's}{distance}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ (3)/(8)&(3)/(5)\\\\ m&(5)/(5) \end{array}\implies \cfrac{\quad(3)/(8) \quad }{m}=\cfrac{(3)/(5)}{(5)/(5)}\implies \cfrac{\quad(3)/(8) \quad }{(m)/(1)}=\cfrac{(3)/(5)}{(5)/(5)}`


`\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`