Question

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

Answer 1

Using the Pythagorean theorem, we can determine that the eastbound car had traveled 24 miles when the northbound car had traveled 18 miles with the distance between them being 6 miles more than what the eastbound car had traveled.

Step-by-step explanation:

When a car travels north and another travels east from the same intersection, the path they create forms a right-angled triangle, with their paths being the two perpendicular sides. In this scenario, the car traveling north has gone 18 miles. If we denote the distance the eastbound car has traveled as x miles, the hypotenuse (the distance between the two cars) is x + 6 miles. Using the Pythagorean theorem:
182 + x2 = (x + 6)2
Solving this equation gives us the distance traveled by the eastbound car. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides:
324 + x2 = x2 + 12x + 36
After simplifying, this leaves us with 12x = 288, so x = 24. Therefore, the eastbound car had traveled 24 miles.