https://file.aiquickdraw.com/mathbot/file/17303584899576ccfhjf2.jpg

Let's solve this step by step.

Let:
- \( d \) be the distance Nicole runs.

According to the problem, Nicole’s friend runs \( \frac{4}{7} \) of a mile, and this distance is \( \frac{4}{5} \) of Nicole’s distance. Thus, we can set up the equation:

\[
\frac{4}{7} = \frac{4}{5} \times d
\]

To isolate \( d \), divide both sides by \( \frac{4}{5} \):

\[
d = \frac{4}{7} \div \frac{4}{5}
\]

Dividing by a fraction is the same as multiplying by its reciprocal, so:

\[
d = \frac{4}{7} \times \frac{5}{4}
\]

The \( 4 \)s cancel out, leaving:

\[
d = \frac{5}{7}
\]

So, Nicole runs \( \frac{5}{7} \) of a mile.

Would you like further details or have any questions?

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### Related Questions:
1. How would the solution change if Nicole’s friend ran \( \frac{3}{4} \) of a mile?
2. What if Nicole’s friend’s distance was \( \frac{3}{5} \) of Nicole’s?
3. How can we verify the solution by substituting the values back?
4. How would the setup differ if Nicole's friend ran a full mile?
5. Can this problem be solved using proportions?

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**Tip:** To solve equations involving fractions, try converting division into multiplication with the reciprocal to simplify calculations.

Nicole’s friend runs 4/7 of a mile, but her distance is only 4/5 of Nicole’s distance. How far does Nicole run?

Learn how to solve a problem where Nicole’s friend runs 4/7 of a mile, which is only 4/5 of Nicole's distance. This solution covers key algebraic concepts, including fraction multiplication and division. Suitable for students in Grades 6-8.

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