Question

a woman can hike 2 miles faster down a trail to Archuletta Lake then she can on the return trip uphill. it takes her 2 hours to get to the lake and 4 hours to return. what is her speed hiking down to the lake?

Answer 1

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

$\begin{gathered} \frac{D}{2}-\frac{D}{4}=2 \\ \frac{2D}{4}-\frac{D}{4}=2 \\ \frac{D}{4}=2 \\ D=8 \end{gathered}$

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