Question 893899
Things we need to know to solve this:
1. Distance = rate * time
2. {{{a^2+b^2=c^2}}}<br>

First we need to find the distance that each individual car went.  To do that we use the first formula I listed.  <br>

Distance car 1 went:
Distance = rate * time
Distance = 100 km/hour * 2 hours
Distance = 200 km<br>

Distance Car 2 went:
Distance = rate * time
Distance = 50 km/hour * 2 hours
Distance = 100 km<br>

Now lets stop to think about this for a minute.  One car went south and the other went west.  We can think about those distances traveled as legs of a right triangle.  The distance between them would then be the hypotenuse of the triangle.  So now that we know the distance both cars went(the lengths of the legs of the right triangle) we can use equation 2 listed above(the Pythagorean theorem) to find their distance apart(the hypotenuse of the right triangle).<br>

{{{(Distance apart)^2 = (distance car 1 went)^2 + (distance car 2 went)^2}}}
{{{(Distance apart)^2 = (200)^2 + (100)^2}}}
{{{(Distance apart)^2 = 40000 + 10000}}}
{{{(Distance apart)^2 = 50000}}}
{{{Distance apart = sqrt(50000)}}}
{{{Distance apart = 100*sqrt(5)}}}
Distance apart = 223.6067977 km