Problem: My neighborhood is full of one-way streets. To drive from my house to the grocery store, I have to go 1 block south, then 1 block east, then 5 blocks north, then 2 blocks east. Each block is $\frac{1}{16}$ of a mile. How much shorter would my trip be if I could fly like a bird?

Let's start by calculating length of a trip:
1 block + 1 block + 5 blocks + 2 blocks = 9 blocks
Each block is 1/16 miles so total length of a trip is:
9 * 1/16 = 9/16 mile

To find distance bird would fly we need to find coordinates of final point. We assume that we start at (0,0). For east and north directions we would use positive numbers and for west and south directions we would use negative numbers.
After moving one block to south we are at (0,-1).
Then we move one block to east we are at (1,-1).
Then we move 5 blocks to north and we are at (1,4).
Then we move 2 blocks to east and we are at (3,4).

Now we need to find distance between ending point and starting point.
Formula is:
[tex]d= \sqrt{ ( x_{2}- x_{1} )^{2} +(y_{2}- y_{1} )^{2} } [/tex]
[tex]d=\sqrt{ ( 3- 0 )^{2} +(4- 0 )^{2} } [/tex]
[tex]d= \sqrt{9+16} [/tex]
[tex]d= \sqrt{25} =5[/tex]
Bird would need to fly 5 blocks or 5 * 1/16 = 5/16 miles

We need to find out how much shorter trip would fly a bird:
9/16 - 5/16 = 4/16 = 1/4
Bird would fly 1/4mile shorter trip.