\begin{tabular}{|l}\hline 5. A park bench is located $$ 163 / 4 $$ feet north of an \ elm tree. A water fountain is located $$ 91 / 2 $$ feet \ due south of the same elm tree. \end{tabular} $$ \begin{array}{l} ext { What is the distance in feet between the park } \ ext { Wench and the water fountain? }\end{array} $$

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\begin{tabular}{|l}\hline 5. A park bench is located $$ 163 / 4 $$ feet north of an \ elm tree. A water fountain is located $$ 91 / 2 $$ feet \ due south of the same elm tree. \end{tabular} $$ \begin{array}{l}	ext { What is the distance in feet between the park } \ 	ext { Wench and the water fountain? }\end{array} $$

UpStudy AI · Accepted Answer

To determine the distance between the park bench and the water fountain, let's analyze their positions relative to the elm tree.

1. **Position of the Park Bench:**
   - The bench is located $$ \frac{163}{4} $$ feet north of the elm tree.
   - $$ \frac{163}{4} = 40.75 $$ feet.

2. **Position of the Water Fountain:**
   - The fountain is located $$ \frac{91}{2} $$ feet south of the elm tree.
   - $$ \frac{91}{2} = 45.5 $$ feet.

3. **Calculating the Total Distance:**
   - Since the bench is north and the fountain is south of the same tree, the total distance between them is the sum of their individual distances from the tree.
   $$
   \text{Total Distance} = 40.75 \, \text{feet} + 45.5 \, \text{feet} = 86.25 \, \text{feet}
   $$
   - Alternatively, using fractions:
   $$
   \frac{163}{4} + \frac{91}{2} = \frac{163}{4} + \frac{182}{4} = \frac{345}{4} = 86 \frac{1}{4} \, \text{feet}
   $$

**Final Answer:**
The distance between the park bench and the water fountain is $$ 86\,\frac{1}{4} $$ feet.
The distance between the park bench and the water fountain is $$ 86\,\frac{1}{4} $$ feet.

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