### Instruction: Eugene, Brianna, and Katie are going on a run. Eugene runs at a rate of 4 miles per hour. If Brianna runs $\frac{2}{3}$ as fast as Eugene, and Katie runs $\frac{7}{5}$ as fast as Brianna, how fast does Katie run?### Response: I need to find Katie's running speed in miles per hour.
To do that, I need to find Brianna's running speed first, since Katie's speed is given in terms of Brianna's.
Brianna runs $\frac{2}{3}$ as fast as Eugene, who runs at 4 miles per hour.
That means Brianna runs $\frac{2}{3} \times 4$ miles per hour, which is $\frac{8}{3}$ miles per hour.
Now I can use this to find Katie's speed.
Katie runs $\frac{7}{5}$ as fast as Brianna, who runs at $\frac{8}{3}$ miles per hour.
That means Katie runs $\frac{7}{5} \times \frac{8}{3}$ miles per hour, which is $\frac{56}{15}$ miles per hour.
This is the final answer.