We will use the notation: 

North = UP, South = DOWN, East = RIGHT, West = LEFT

We will indicate the first runner's path with green arrows,
starting at point P:

>>One heads south at 7 mph for 3 hours...<< 

So he or she goes 7×3 or 21 miles DOWNWARD from point P,
like this:



>>and then heads east at 5 mph for 1 hour.<<

So he or she turns and goes 5×1 or 5 miles TO THE RIGHT,
like this:




>> The other friend heads west for two hours at 6 mph <<

So he or she goes 2×6 or 12 miles LEFT from point P.


We will indicate the other runner's path with red arrows,
starting a point P, like this:



>>and then heads north at 5 mph for 2 hours.<<

So he or she turns and goes 5×2 or 10 miles UP,
like this: 



So at the end of 4 hours the first runner is at the end of
the green path and the other runner is at the end of the red path.
We want to know how far they are apart, so let's draw a blue line
between where the runners are after 4 hours:



Now we'll draw a horizontal and vertical black line so that the
blue line will be the hypotenuse of a big right triangle, like this:



We'll draw two points on the black lines directly
above and directly to the right of point P, like this:



Now we can see that the upper horizontal side of the big
right triangle is 12+5 or 17 miles and the vertical side
of the big right triangle is 10+21 or 31 miles.  Therefore
we can use the Pythagorean theoren and find the distance
between the runners (the blue line), which is the hypotenuse
of the big right triangle:

(distance between runners)² = 17² + 31²
(distance between runners)² = 289 + 961
(distance between runners)² = 1250
   distance between runners = √1250
   distance between runners = √625·2
   distance between runners = 25√2
   distance between runners is approximately 35.35533906 miles, which
you should round off as your teacher desires, perhaps to 35.4 miles.
   

Edwin