Question: Current Skill $ A fountain is located 34\frac{3}{4} feet due east of a basketball court. A…

Current Skill $ A fountain is located 34\frac{3}{4} feet due east of a basketball court. A playground is located 29\frac{5}{8} feet due west of that same basketball court. What is the distance in feet between the fountain and the playground?

Solution

To solve this problem, we need to find the total distance between the fountain and the playground. The fountain is 34\(\frac{3}{4}\) feet east of the basketball court, and the playground is 29\(\frac{5}{8}\) feet west of the same basketball court. The distance between them is the sum of these two distances: Convert the mixed numbers into improper fractions. 34\(\frac{3}{4}\) is converted to: \[ 34 + \frac{3}{4} = \frac{136}{4} + \frac{3}{4} = \frac{139}{4} \] 29\(\frac{5}{8}\) is converted to: \[ 29 + \frac{5}{8} = \frac{232}{8} + \frac{5}{8} = \frac{237}{8} \] Now we need a common denominator to add these fractions. The least common denominator of 4 and 8 is 8. Convert \(\frac{139}{4}\) to a fraction with denominator 8: \[ \frac{139}{4} = \frac{139 \times 2}{4 \times 2} = \frac{278}{8} \] Add the distances: \[ \frac{278}{8} + \frac{237}{8} = \frac{515}{8} \] Convert \(\frac{515}{8}\) back to a mixed number: \[ \frac{515}{8} = 64 \frac{3}{8} \] The distance between the fountain and the playground is 64\(\frac{3}{8}\) feet.