Question
How do I calculate the distance traveled by a person who walked east and then west?
Answers
GPT-4o mini
To calculate the distance traveled by a person who walked east and then west, you can follow these steps:
1. **Determine the Distance Traveled in Each Direction**: Measure or note the distance the person walked east (let’s call this distance \(d_{east}\)) and the distance walked west (let’s call this distance \(d_{west}\)).
2. **Total Distance Traveled**: The total distance traveled is simply the sum of the distances walked in each direction. This can be calculated using the following formula:
\[
\text{Total Distance} = d_{\text{east}} + d_{\text{west}}
\]
For example, if a person walked 5 miles east and then 3 miles west, the calculation would be:
- Distance east: \(d_{east} = 5\) miles
- Distance west: \(d_{west} = 3\) miles
Calculating the total distance traveled:
\[
\text{Total Distance} = 5 \text{ miles} + 3 \text{ miles} = 8 \text{ miles}
\]
So, the person traveled a total of 8 miles.
Remember, this total includes all the walking regardless of the direction, so it does not take into account the person's final position relative to their starting point. If you want to find the net displacement (the straight-line distance from the starting point to the ending point), you would subtract the distance walked west from the distance walked east:
\[
\text{Net Displacement} = d_{\text{east}} - d_{\text{west}}
\]
In the example above, the net displacement would be:
\[
\text{Net Displacement} = 5 \text{ miles} - 3 \text{ miles} = 2 \text{ miles} \text{ east}
\]
This gives you an idea of how far the person is from their original starting point.
1. **Determine the Distance Traveled in Each Direction**: Measure or note the distance the person walked east (let’s call this distance \(d_{east}\)) and the distance walked west (let’s call this distance \(d_{west}\)).
2. **Total Distance Traveled**: The total distance traveled is simply the sum of the distances walked in each direction. This can be calculated using the following formula:
\[
\text{Total Distance} = d_{\text{east}} + d_{\text{west}}
\]
For example, if a person walked 5 miles east and then 3 miles west, the calculation would be:
- Distance east: \(d_{east} = 5\) miles
- Distance west: \(d_{west} = 3\) miles
Calculating the total distance traveled:
\[
\text{Total Distance} = 5 \text{ miles} + 3 \text{ miles} = 8 \text{ miles}
\]
So, the person traveled a total of 8 miles.
Remember, this total includes all the walking regardless of the direction, so it does not take into account the person's final position relative to their starting point. If you want to find the net displacement (the straight-line distance from the starting point to the ending point), you would subtract the distance walked west from the distance walked east:
\[
\text{Net Displacement} = d_{\text{east}} - d_{\text{west}}
\]
In the example above, the net displacement would be:
\[
\text{Net Displacement} = 5 \text{ miles} - 3 \text{ miles} = 2 \text{ miles} \text{ east}
\]
This gives you an idea of how far the person is from their original starting point.