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A woman has a new fitness watch. She uses this formula to calculate her step length:
[tex]\[ \text{Step length (feet)} = \frac{\text{measured distance in feet}}{\text{number of steps taken}} \][/tex]
Her measured distance was 20 feet, and the number of steps taken was 16. In her first week, she walked 67,118 steps. How many kilometers did she walk in the first week?
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.
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