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physlexic

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## Homework Statement

Problem reads:

In reaching her destination, a backpacker walks with an average velocity of 1.34 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.68 m/s, due west, turns around, and hikes with an average velocity of 0.447 m/s, due east. How far east did she walk?

## Homework Equations

Vavg = delta X/ delta t

## The Attempt at a Solution

I let

vw= average velocity from hiking west

xw = west displacement

tw = the time it took to travel in the west direction

ve = average velocity from hiking east

xe = east displacement

te = the time it took to travel in the east directionvw = 2.68 m/s

xw = 6.44 km = 6440 m

tw = 6440 m / 2.68 m/s = 2403 s

ve = 0.447 m/s

xe = ?

te = ?

using the avg. velocity equation as ve = xe / te I solve for xe where ve = 0.447 m/s

xe = te * 0.447 m/stherefore according to the equation Vavg = xe-xw / te-tw

However, I'm looking at other solutions and it shows the equation to be Vavg = xw + xe / te + te

I thought average velocity is a change in displacement over a change in time? So why are they adding the displacement & time as opposed to subtracting? So confused...

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