Question 268067
Hi Nora---
Lets see what we can do:
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

Let d=distance that the northbound car travelled

Now know that we have a right triangle to deal with here and the distance between the two cars is the hypotenuse of the right triangle. 
The base of the right triangle (car travelling east) is 15 mi; the hypotneuse is (d+5) and the other side is d(car travelling north).

Applying the pythagorean theorem, we have:
(d+5)^2=15^2+d^2 expand the left side and simplify
d^2+10d+25=225+d^2 subtract d^2 and also 25 from each side
d^2-d^2+10d+25-25=225-25+d^2-d^2 collect like terms
10d=200 divide each side by 10
d=20 mi-------------------distance travelled by northbound car

distance between the cars=d+5=20+5=25 mi

CK
25^2=15^2+20^2
625=225+400
625=625

Does this help?---ptaylor