Two cars leave an intersection One car travels east the othe

Two cars leave an intersection. One car travels east; the other north. when the car traveling east had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading north. How far had the northbound car traveled?

Solution

The distance between the cars is the hypotenuse of the right triangle formed by the 2 distances from the intersection.
E = 15 (eastbound car)
d^2 = E^2 + N^2
d = N + 5
(N+5)^2 = 15^2 + N^2
N^2 + 10N + 25 = 225 + N^2
10N = 200
N = 20 miles