Sure, let's go through the process step by step to find out how many kilometers she walked in the first week.
1. Calculate the Step Length:
We are given the measured distance and the number of steps taken to measure that distance. According to the formula:
[tex]\[
\text{Step length} (\text{feet}) = \frac{\text{distance} (\text{feet})}{\text{steps taken}}
\][/tex]
Plugging in the given values:
[tex]\[
\text{Step length} (\text{feet}) = \frac{20 \text{ feet}}{16 \text{ steps}} = 1.25 \text{ feet per step}
\][/tex]
2. Calculate the Total Distance Walked in Feet:
We know that she walked 67118 steps in the first week. Using her step length, we can calculate the total distance walked:
[tex]\[
\text{Total distance} (\text{feet}) = \text{step length} (\text{feet per step}) \times \text{number of steps}
\][/tex]
[tex]\[
\text{Total distance} (\text{feet}) = 1.25 \text{ feet per step} \times 67118 \text{ steps} = 83897.5 \text{ feet}
\][/tex]
3. Convert the Total Distance from Feet to Kilometers:
We know the conversion factor between feet and kilometers: [tex]\(1 \text{ foot} = 0.0003048 \text{ kilometers}\)[/tex]. To convert the total distance walked in feet to kilometers, we use this conversion factor:
[tex]\[
\text{Total distance} (\text{kilometers}) = 83897.5 \text{ feet} \times 0.0003048 \frac{\text{kilometers}}{\text{foot}}
\][/tex]
[tex]\[
\text{Total distance} (\text{kilometers}) = 25.571958 \text{ kilometers}
\][/tex]
So, the woman walked approximately 25.571958 kilometers in the first week.
