cars traveling

Question

Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 18 miles, the distance between the cars was 6 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled.

Answer 1

Let East = The distance by traveled the car heading east

Let North = The distance traveled by the car heading north

 

Since east and north are at a right angle to one another, East and North are the legs of a right triangle and the Distance_between_them is the hypotenuse.  Apply the Pythagorean Theorem:

 

East² + North² = (Distance between them)²

 

Since North=18 miles and Distance_between_them = East+6:

 

East² + 18² = (East + 6)²

 

East² + 324 = East² + 12East + 36

 

288 = 12*East

 

Solve for East

Answer 2

Let x = east bound car's distance

 

Let x + 6 = distance between cars. Use Pythagorean Theorem

 

x^2 + 18^2 = (x+6)^2

 

x^2 + 324 = x^2 + 12x + 36

 

12x + 36 = 324

 

12x = 288

 

x = 24 miles