Question

using the paths shown, how long is the shortest route from springdale to riverside?
diagram with points: springdale, greenpoint, cedarburg, riverside. paths: springdale to greenpoint: (12 \frac{7}{8}) mi, greenpoint to riverside: (14 \frac{3}{8}) mi, greenpoint to cedarburg: 7 mi, cedarburg to riverside: (8 \frac{1}{4}) mi.
write your answer as a fraction or as a whole or mixed number.
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Explanation:

Step1: Identify two possible routes

First, find the length of the direct route from Springdale to Greenpoint to Riverside: $12\frac{7}{8} + 14\frac{3}{8}$. Second, find the length of the route through Cedarburg: $12\frac{7}{8} + 7 + 8\frac{1}{4}$. Then compare the two lengths.

Step2: Calculate the first route length

Convert mixed numbers to improper fractions or add the whole and fractional parts separately.
$12\frac{7}{8} + 14\frac{3}{8} = (12 + 14) + (\frac{7}{8} + \frac{3}{8}) = 26 + \frac{10}{8} = 26 + 1\frac{2}{8} = 27\frac{1}{4}$ miles.

Step3: Calculate the second route length

First, convert $8\frac{1}{4}$ to eighths: $8\frac{2}{8}$. Then add:
$12\frac{7}{8} + 7 + 8\frac{2}{8} = (12 + 7 + 8) + (\frac{7}{8} + \frac{2}{8}) = 27 + \frac{9}{8} = 27 + 1\frac{1}{8} = 28\frac{1}{8}$ miles.

Step4: Compare the two route lengths

$27\frac{1}{4}$ (which is $27\frac{2}{8}$) is less than $28\frac{1}{8}$ (which is $28\frac{1}{8}$). So the shortest route is the first one, $27\frac{1}{4}$ miles.

Answer:

$27\frac{1}{4}$