Question 955279
let x=distance of northbound car; x+7=eastbound car
{{{x^2+(x+7)^2=13^2}}}
{{{x^2+x^2+14x+49=169}}} Subtract 169 from each side.
{{{2x^2+14x-120=0}}} Divide each side by 2.
{{{x^2+14x-120=0}}}
{{{(x-5)(x+12)=0}}}
x-5=0  or x+12=0
x=5 ANSWER 1: The northbound car traveled 5 miles.
x+7=5+7=12 mi ANSWER 2: The eastbound car traveled 12 miles.
CHECK: 
They were separated by 13 miles
{{{13^2mi^2=5^2mi^2+12^2mi^2}}}
{{{169mi^2=25mi^2+144mi^2}}}
{{{169mi^2=169mi^2}}}