Question

using the paths shown, how long is the shortest route from fairfax to brookfield? write your answer as a fraction or as a whole or mixed number.

Explanation:

Step1: List possible routes

There are two main possible routes from Fairfax to Brookfield. Route 1: Fairfax - Greenville - Brookfield with distances $\frac{1}{10}$ mi and $\frac{3}{20}$ mi respectively. Route 2: Fairfax - Greenville - Arlington - Brookfield with distances $\frac{1}{10}$ mi, $\frac{3}{5}$ mi and $\frac{9}{20}$ mi respectively.

Step2: Calculate distance of Route 1

Add the distances of the segments of Route 1. $\frac{1}{10}+\frac{3}{20}=\frac{2 + 3}{20}=\frac{5}{20}=\frac{1}{4}$ mi.

Step3: Calculate distance of Route 2

Add the distances of the segments of Route 2. First, find a common - denominator. $\frac{1}{10}+\frac{3}{5}+\frac{9}{20}=\frac{2+12 + 9}{20}=\frac{23}{20}=1\frac{3}{20}$ mi.

Step4: Compare distances

Since $\frac{1}{4}=\frac{5}{20}$ and $\frac{5}{20}<\frac{23}{20}$, the shortest route is Fairfax - Greenville - Brookfield with a distance of $\frac{1}{4}$ mi.

Answer:

$\frac{1}{4}$