How Far Did the Backpacker Walk East?

[triplel777]

Homework Statement

In reaching her destination, a backpacker walks with an average velocity of 1.33 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.60 m/s, due west, turns around, and hikes with an average velocity of 0.425 m/s, due east. How far east did she walk?

Homework Equations

The Attempt at a Solution

average V= delta r/delta t. since i don't know the time i found that first using v= d/t. 2.6= 6.44/t. t=2.48. using that i set up the equation saying 1.33= 2.6-0.425/2.48-t_0 and solved for t_0 which got me 0.844 and since we are looking for a distance i said v= d/t so 0.425= d/0.844= 0.3587 km...but its wrong

 

[rl.bhat]

If d is the distance traveled due east, time taken will be d/0.425 = 2.35*d s.
The average velocity 1.33 = (6440 - d)/(6440/2.6 + 2.35*d)
Now solve for d.

 

[triplel777]

d/0.425 = 2.35*d
it will give me d/d = 5.53 which i don't understand and where does the 2.35 come from?

 

[rl.bhat]

it will give me d/d = 5.53
How did you get this one?

 

[triplel777]

sorry i wrote the wrong number. well you gave me the equation d/0.425 = 2.35*d so 2.35d*0.425=d : d=0.99875d. so d/d=099875 ??

 

[rl.bhat]

sorry i wrote the wrong number. well you gave me the equation d/0.425 = 2.35*d so 2.35d*0.425=d : d=0.99875d. so d/d=099875 ??

No. It is not correct.
Go through #2. again. I have done sum editing.
Solve for d.

 

[triplel777]

If d is the distance traveled due east, time taken will be d/0.425 = 2.35*d s.

How can the variable d be on both sides of the equation?

The average velocity 1.33 = (6440 - d)/(6440/2.6 + 2.35*d)
Now solve for d.

is this suppose to be a fraction over a fraction?

 

[rl.bhat]

is this suppose to be a fraction over a fraction?

No. It is
1.33 = (6440 - d)/(2477 + 2.35d)

 

[triplel777]

1.33 = (6440 - d)/(2477 + 2.35d)

so
1.33*(2477+2.35d)= 6440-d
3294.41+3.126d= 6440-d
-3145.59+3.126d= -d
? what do i do from there?

 

[rl.bhat]

so
1.33*(2477+2.35d)= 6440-d
3294.41+3.126d= 6440-d
-3145.59+3.126d= -d
? what do i do from there?

3145.59 = 3.126d + d

 

[triplel777]

3145.59 = 3.126d + d

ok so if i add 3.126d+d then that gives me 4.126d
so 3145.59= 4.126d
3145.59/4.126=d
d= 762.94
but that's wrong...?

 

[rl.bhat]

1.33 = (6440 - d)/(2477 + 2.35d)

Rewrite this step.
1.33 = (6440 - d)/(2462 + 2.353d)
Now calculate.

 

[triplel777]

1.33*(2462+2.353d)= 6440-d
3274.46+3.129d= 6440-d
-3165.54+3.129d= -d
3165.54= d+ 3.129d
3165.54= 4.129d
d= 766.7
but that's wrong...