SOLUTION: kristen and katie take a hike on a mountain trail and return on that same trail to the campground from which they started. If they were gone six hours and their average rates were

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Question 1013187: kristen and katie take a hike on a mountain trail and return on that same trail to the campground from which they started. If they were gone six hours and their average rates were 4mph out and 2mph back, how far along the trail did they hike?
Found 3 solutions by ikleyn, josgarithmetic, josmiceli:
Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.
kristen and katie take a hike on a mountain trail and return on that same trail to the campground from which they started. If they were gone six hours and their average rates were 4mph out and 2mph back, how far along the trail did they hike?
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Let d be the distance they hike (in each direction), in miles.

For one direction they spent d%2F4 hours.

For the other direction they spent d%2F2 hours.

Your equation is 

d%2F4+%2B+d%2F2 = 6.

Solve it yourself.

The answer is: d = 8 miles.


Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
            rate        time         distance
OUT          4           x            d
BACK         2           y            d
Total                    6           2d


system%284x=d%2C2y=d%2Cx%2By=6%29-------three equations in three unknown variables, x, y, d.

To begin handling the system, y=6-x;
system%284x=d%2C2%286-x%29=d%29
...and maybe you can do the rest.


---
d=8

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the one-way distance of the trail
Let +t+ = time in hours for the 1st one-way trip
+6+-+t+ = time in hours for the 2nd one-way trip
--------------------------
Equation for the 1st trip:
(1) +d+=+4t+
Equation for the 2nd trip:
(2) +d+=+2%2A%28+6+-+t+%29+
---------------------
Substitute (1) into (2)
(2) +4t+=+2%2A%28+6+-+t+%29+
(2) +4t+=+12+-+2t+
(2) +6t+=+12+
(2) +t+=+2+
---------------
(1) +d+=+4t+
(1) +d+=+4%2A2+
(1) +d+=+8+
The hiked 8 miles in and 8 miles out
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check:
(2) +d+=+2%2A%28+6+-+t+%29+
(2) +d+=+2%2A%28+6+-+2+%29+
(2) +d+=+2%2A4+
(2) +d+=+8+
OK