Assume that her speed down is x
Then her speed up is x - 2/h
Because she is faster by 2 miles down
Since D = S x T, where
D is the distance and S is the speed, T is the time
Her time up is 4 hours, and her time down is 2 hours
Her speed up = D/4
Her speed down = D/2
Since her speed down is faster by 2 miles, then
[tex]\begin{gathered} \frac{D}{2}-\frac{D}{4}=2 \\ \frac{2D}{4}-\frac{D}{4}=2 \\ \frac{D}{4}=2 \\ D=8 \end{gathered}[/tex]The distance between up and down is 8 miles
Her speed down = 8/2 = 4 miles per hour
Her speed hiking down to the lake is 4 miles/hour