A difficult 1D kinematics problem dealing with displacement and velocity

[kathypoot]

In reaching her destination, a backpacker walks with an average velocity of 1.31 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.54 m/s, due west, turns around, and hikes with an average velocity of 0.475 m/s, due east. How far east did she walk?


Is there not enough information? I feel like they should have given me another variable or something.


I figured out that it took her 2535.433 seconds to hike for the 6.55km stretch. But I'm really in the dark on this one, I appologize. I've looked all over the internet to try and find a problem simular to this one but I had no luck.

 

[Hootenanny]

In reaching her destination, a backpacker walks with an average velocity of 1.31 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.54 m/s, due west, turns around, and hikes with an average velocity of 0.475 m/s, due east. How far east did she walk?


Is there not enough information? I feel like they should have given me another variable or something.


I figured out that it took her 2535.433 seconds to hike for the 6.55km stretch. But I'm really in the dark on this one, I appologize. I've looked all over the internet to try and find a problem simular to this one but I had no luck.

Welcome to Physics Forums.

There is sufficient information to solve the problem.

HINT: What is the definition of average velocity?

 

[kathypoot]

Distance/time = average velocity

D/T = 1.31

t1 = time walking west
t2 = time walking east
d1 = distance walked west = 6.44 km = 6440 meters
d2 = distance walked east

T = t1 + t2
D = d1 - d2

t1 = distance/speed = 6440/2.54 = 2535.4 seconds

t2 = d2/v2 = d2/0.475
so d2 = 0.475*t2

Now use all this in the equation for D/T.
D/T = (d1 - d2)/(t1 + t2) = 1.31
(6440 - 0.475*t2)/(2535.4 + t2) = 1.31
6440 - 0.475*t2 = 3321.42 + 1.31*t2
1.786*t2 = 3118.58
t2 = 1747.11 seconds

d2 = t2*v2 = 829.87

Check by calculating the displacement and time and then seeing if we get the average velocity we started with.
displacement = d1 - d2 = 5610.13 meters
time = t1 + t2 = 4282.54 seconds
average speed = displacement/time = 5610.13/4282.54 = 1.31 m/s

So she walked 5610.13 meters (or 5.61 km) east



but my answer is still wrong... :(

 

[Jebus_Chris]

What you did is correct. The question is asking for how far east she traveled. That would be d2, 829, not 5610 which is the total displacement which 5610m west.