Sure, let's work through the problem step by step.
1. Calculate the Step Length in Feet:
The step length is found by dividing the measured distance by the number of steps taken.
[tex]\[
\text{Step length (feet)} = \frac{\text{Measured distance}}{\text{Number of steps taken}}
\][/tex]
Given:
- Measured distance = 20 feet
- Number of steps taken = 16
So,
[tex]\[
\text{Step length (feet)} = \frac{20 \text{ feet}}{16 \text{ steps}} = 1.25 \text{ feet/step}
\][/tex]
2. Calculate the Total Distance Walked in Feet:
To find the total distance walked in a week, multiply the total number of steps by the step length.
[tex]\[
\text{Total distance (feet)} = \text{Total week steps} \times \text{Step length (feet)}
\][/tex]
Given:
- Total week steps = 67118 steps
- Step length = 1.25 feet/step
So,
[tex]\[
\text{Total distance (feet)} = 67118 \text{ steps} \times 1.25 \text{ feet/step} = 83897.5 \text{ feet}
\][/tex]
3. Convert the Distance from Feet to Kilometers:
Use the conversion factor to change feet into kilometers.
[tex]\[
1 \text{ foot} = 0.0003048 \text{ kilometers}
\][/tex]
So,
[tex]\[
\text{Total distance (kilometers)} = \text{Total distance (feet)} \times 0.0003048 \text{ kilometers/foot}
\][/tex]
Given:
- Total distance (feet) = 83897.5 feet
So,
[tex]\[
\text{Total distance (kilometers)} = 83897.5 \text{ feet} \times 0.0003048 \text{ kilometers/foot} = 25.571958 \text{ kilometers}
\][/tex]
Therefore, the total distance she walked in the first week is approximately 25.571958 kilometers.
