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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 (that is, travel in a straight line)?

Explain your solution, and give your answer in miles.

 Mar 17, 2019
 #1
avatar+102417 
+1

Let's suppose that your house is  located at (0,0)

1 block south from here puts you at (0, -1/16)

1 block east from here now puts you at (1/16, -1/16)

5 blocks north from here puts you at  (1/16, 4/16)

2 blocks east from here puts you at (3/16, 4/16)

 

You have traveled  (1/16)  ( 1 + 1 + 5 + 2) =   9 / 16 of a mile

 

The "straightline" distance between (0, 0)  and (3/16, 4/16) = 

 

sqrt  [ (3/16^2 + (4/16)^2 ]  =   sqrt [  25 / 256]  =   5 /16  of a mile

 

So....your trip  would be  [ 9/16 - 5/16 ]   =  4/16 =  1/4  of a mile shorter

 

 

cool cool cool

 Mar 17, 2019
 #2
avatar+4299 
+4

First, I advise you to draw this on a coordinate plane. The bird travels 9 blocks, for a total of 9*1/16=9/16 miles.

Starting Point: (0,0). 

Next Point: (0, -1)

Next Point: (1, -1)

Next Point: (1, 4)

Final Point: (3, 4)

 

Use the distance formula from (0,0) to (3,4) to get a result of 5, so 5*1/16=5/16 miles.

 

Thus, the answer should be 9/16-5/16=4/16=1/4 of a mile shorter.

 Mar 17, 2019

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