Starting from the front door of your ranch house, you walk 60.0 m due east to your windmill, turn around, and then slowly walk 40.0 m west to a bench, where you sit and watch the sunrise. It takes you 29.0 s to walk from your house to the windmill and then 42.0 s to walk from the windmill to the bench. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Average and instantaneous velocities.

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To solve this problem, we need to find the average velocity of the person walking from the front door of the ranch house to the bench.

Given:
- Distance from the front door to the windmill = 60.0 m
- Distance from the windmill to the bench = 40.0 m
- Time taken to walk from the front door to the windmill = 29.0 s
- Time taken to walk from the windmill to the bench = 42.0 s

The average velocity is calculated using the formula:
$$ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} $$

First, we need to find the total displacement. Since the person walks 60.0 m due east and then 40.0 m west, the total displacement is the difference between the eastward and westward distances:
$$ \text{Total Displacement} = 60.0 \, \text{m} - 40.0 \, \text{m} = 20.0 \, \text{m} $$

Next, we calculate the total time taken for the entire journey:
$$ \text{Total Time} = 29.0 \, \text{s} + 42.0 \, \text{s} = 71.0 \, \text{s} $$

Now, we can calculate the average velocity:
$$ \text{Average Velocity} = \frac{20.0 \, \text{m}}{71.0 \, \text{s}} $$

Let's calculate the average velocity.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{20}{71}$$
The average velocity of the person walking from the front door of the ranch house to the bench is approximately 0.28169 m/s.
The average velocity is approximately 0.28 m/s east.

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