SOLUTION: In reaching her destination, a backpacker walks with an average velocity of 1.10 m/s, due west. This average velocity results, because she hikes for 5.61 km with an average velocit

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: In reaching her destination, a backpacker walks with an average velocity of 1.10 m/s, due west. This average velocity results, because she hikes for 5.61 km with an average velocit      Log On

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Question 1145152: In reaching her destination, a backpacker walks with an average velocity of 1.10 m/s, due west. This average velocity results, because she hikes for 5.61 km with an average velocity of 2.77 m/s due west, turns around, and hikes with an average velocity of 0.376 m/s due east. How far east did she walk (in kilometers)?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t%5B1%5D+ = time in seconds for westbound hike
Let +t%5B2%5D+ = time in seconds for eastbound hike
Let +d%5B2%5D+ = distance walked eastward
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The average velocity is [ displacement in meters ] / [ total time in seconds moving ]
(1) +1.1+=+%28+5610+-+d%5B2%5D+%29+%2F+%28+t%5B1%5D+%2B+t%5B2%5D+%29+
-----------------------------------------
For the 1st part of trip:
(2) +5610+=+2.77%2At%5B1%5D+
----------------------------
For the second part of the trip:
(3) +d%5B2%5D+=+.376%2At%5B2%5D+
--------------------------------
There are 3 equations & 3 unknowns, so it's solvable.
(2) +t%5B1%5D+=+2025.27+ sec
--------------------------------
(1) +1.1+=+%28+5610+-+d%5B2%5D+%29+%2F+%28+t%5B1%5D+%2B+t%5B2%5D+%29+
(1) +1.1+=+%28+5610+-+d%5B2%5D+%29+%2F+%28+2025.27+%2B+t%5B2%5D+%29+
(1) +1.1+=+%28+5610+-+.376%2At%5B2%5D+%29+%2F+%28+2025.27+%2B+t%5B2%5D+%29+
(1) +1.1%2A%28+2026.27+%2B+t%5B2%5D+%29+=+5610+-+.376%2At%5B2%5D+
(1) +2227.8+%2B+1.1t%5B2%5D+=+5610+-+.376%2At%5B2%5D+
(1) +1.476t%5B2%5D+=+3382.2+
(1) +t%5B2%5D+=+2291.46+ sec
---------------------------------
(3) +d%5B2%5D+=+.376%2At%5B2%5D+
(3) +d%5B2%5D+=+.376%2A2291.46+
(3) +d%5B2%5D+=+323.96+
In km:
(3) +d%5B2%5D+=+323.96%2F1000+
(3) +d%5B2%5D+=+.324+ km
---------------------------------
check:
(1) +1.1+=+%28+5610+-+d%5B2%5D+%29+%2F+%28+t%5B1%5D+%2B+t%5B2%5D+%29+
(1) +1.1+=+%28+5610+-+323.96+%29+%2F+%28+2025.27+%2B+2291.46+%29+
(1) +1.1+=+5286.04+%2F+4316.73+
(1) +1.1+=+1.224+
Answer is off. I think method is OK. Check the math