Mary walks 4 miles north and then turns and walks 5 miles west. how far is she from her original starting point?

 6.403 miles; or, write as:  6.403 mi.  .

Explanation:


                                5

`                             right angle   |_ |
   `          (right triangle )                 |
         `                                               |    4 
             `                                           |
                      `    
       "c"                        `                  \        
 (hypotenuse)                          Starting point
                     

Since we have a "right triangle, we solve for "c"; using the 
"Pythagorean theorem" ; 

→  a² + b² = c² ; Solve for "c" ; our answer (in "miles"; or, "mi.") ;

Given : a = 4; b = 5 ; 

Plug these known values into our equation:

 → 4² + 5² = c² ; 

 → 16 + 25 = c² ;  ↔  c² = 16 + 25 ;

 → c² = 41 ; 

 → Take the positive square root of each side of the equation (since the side of a "triangle" cannot be "negative"; 

 → √(c²) = √(41) ; 

 → c =  √41 ; Use calculator;

 → c =  6.40312423743 ; Round to:  

 → c = 6.403 miles; or, 6.403 mi.