To find the distance traveled by the northbound car, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In this case, the eastbound car's distance (6 miles) is one side (a), the distance traveled by the northbound car is the other side (b), and the straight-line distance between the two cars (7 miles) is the hypotenuse (c). We can set up the equation: a^2 + b^2 = c^2. Plugging in the values, we have 6^2 + b^2 = 7^2, which simplifies to 36 + b^2 = 49. Solving for b^2 gives us b^2 = 49 - 36 = 13. Taking the square root of both sides, we find b = √13, which is approximately 3.6 miles. Therefore, the northbound car has traveled approximately 5.4 miles.