Brandon goes on a ACaub Scout hike and hikes to a waterfall

Brandon goes on a ACaub Scout hike and hikes to a waterfall in 3 hours and hikes back along the same route to the compground in 2 hours. If the hiking rate is 1mph faster returning than going, how fast are the boys hiking each way?

Solution

Let s = hiking rate going
then
(s+1) = hiking rate returning
:
The distance of each trip is the same. Write a distance equation Dist = time * speed.
:
go dist = return dist
3s = 2(s+1)
3s = 2s + 2
3s - 2s = 2
s = 2 mph is the hiking rate going,
:
Obviously, 3 mph is the hiking rate returning
;
:
Check solution by confirming the distances are the same:
3*2 = 6 mi
2*3 = 6 mi