Problem 15.

In reaching her destination, a backpacker walks with an average velocity of 1 m/s, due west. This average velocity results, because she hikes for 6 km with an average velocity of 3 m/s due west, turns around, and hikes with an average velocity of 0.3 m/s due east.

How far east did she walk (in kilometers)?

Solution:

We will define the average velocity as the ratio of total traveled distance and total traveled time (the average velocity can be also defined as the ratio of displacement and traveled time).

The backpacker walks 6km=6000m due to west. The average velocity was 3 m/s. Then the traveled time for this motion is

Then she travels east. Let assume that her traveled time due to east is . Then the traveled distance due to east is

Then the total traveled distance is and the total traveled time is . Then the final average velocity is

From this equation we can find :

Then we can find :