Question

A woman can walk 2mph faster down a trail than she can returning up the trail. It takes her 2 hr to get down and 4 hr to get back up. What is her speed down the trail?

Answer 1

so she goes up the trail
and then down the trail

now the trail doesn't get longer or shorter, thus the distance on both cases is the same
so we can say that

\(\begin{array}{llll}
&\bf distance& \bf rate &\bf time\\
\textit{up the trail}&d& r& 4\\
\textit{down the trail}&d& r+2& 2
\end{array}\)

distance = rate x time

so UP distance and DOWN distance are the same, or equal to each other, thus

d = d
rt = rt => r*4 = (r+2) * 2

# solve for "r" to find the the rate when she's going UP
whatever that gives you, the DOWN rate is THAT MUCH + 2