The hikers started at point S.
The first hiker went 2 miles east and 1 mile north to point A.
The second hiker went 1 mile west and 3 miles south to point B.
See the figure below.
A
I
1 mile I 1 mile
I---------S------------------I
I 2 miles
I
I
3 miles I
I
I
B
Now we need to see how much east and how much north hiker B is from hiker A.
A
I
1 mile I 1 mile
I---------S------------------I
I 2 miles I
I I
I I
3 miles I I 3 miles
I I
I I
B----------------------------I
3 miles
From point B go 3 miles east, then 3 + 1 = 4 miles north to point B.
The distance between the hikers is the hypotenuse of a triangle with legs of lengths 3 and 4.
3^2 + 4^2 = d^2
9 + 16 = d^2
d^2 = 25
d = 5
The distance between the hikers is 5 miles.