A person jogs 4.5 km east in 20 minutes, and then turns around and jogs 1.5 km west in 8 minutes. Calculate average speed and average velocity. For full credit please show your work (PSYW) and include units.

## Step 1<br />The problem involves calculating the average speed and average velocity of a person who jogs 4.5 km east in 20 minutes and then 1.5 km west in 8 minutes.<br /><br />## Step 2<br />The total distance covered by the person is the sum of the distances he jogs east and west. This is calculated as:<br />### \(4.5 \, \text{km} + 1.5 \, \text{km} = 6 \, \text{km}\)<br /><br />## Step 3<br />The total time taken by the person is the sum of the time he spends jogging east and west. This is calculated as:<br />### \(20 \, \text{minutes} + 8 \, \text{minutes} = 28 \, \text{minutes}\)<br /><br />## Step 4<br />The average speed is calculated by dividing the total distance by the total time. This is calculated as:<br />### \(\frac{6 \, \text{km}}{28 \, \text{minutes}} = 0.214 \, \text{km/minute}\)<br /><br />## Step 5<br />The average velocity is calculated by dividing the total displacement by the total time. The displacement is the difference between the distance he jogs east and the distance he jogs west, which is \(4.5 \, \text{km} - 1.5 \, \text{km} = 3 \, \text{km}\) east. This is calculated as:<br />### \(\frac{3 \, \text{km}}{28 \, \text{minutes}} = 0.107 \, \text{km/minute}\)