Verified Answer :

So, doing a guess and check,

Liza's house.

From Liza's house to the Park it is 5\(\frac{1}{2}\) miles.

From the Park to the Library it is also 5\(\frac{1}{2}\) miles.

From the Library to Dan it is 4 miles.

From Dan it is 3 miles back to Liza's house.

So you must add all those together,

5\(\frac{1}{2}\)+5\(\frac{1}{2}\)+4+3

We got lucky because 5\(\frac{1}{2}\)+5\(\frac{1}{2}\) have common denominators.

So,

5\(\frac{1}{2}\)
+
5\(\frac{1}{2}\)

=11     (\(\frac{1}{2}\)+\(\frac{1}{2}\)=1, so 5+5+1)

So that is 11, then, 

11+4+3=18

18 miles total.

This is your route. From Liza's house to the Park, then Library, then Dan's, then back to Liza's house.