#### Answer

Alinna traveled 4 miles farther by using alternative route from A to B

#### Work Step by Step

According to question AC=5 miles and CB=12 miles
$\triangle$ABC is right angled triangle
$AB^{2}$=$AC^{2}$+$CB^{2}$
$AB^{2}$=$5^{2}$+$12^{2}$
$AB^{2}$=25+144
$AB^{2}$=169
AB=$\sqrt 169$=13
Now we have to find how much farther Alinna traveled
so it will be,
AC+CB-AB
5+12-13=4 miles