Final answer:
By treating the paths of the planes as vectors and using the Pythagorean theorem, the calculated distance between the two planes when they land is approximately 159 miles. The provided choices do not include this answer, indicating a possible mistake in the question or the choices.
Step-by-step explanation:
To determine how far apart the two planes are when they land at their respective airports, we can treat their paths as vectors and apply the Pythagorean theorem to find the distance between the two endpoints. The first plane moves 50 miles east and 75 miles north, while the second plane moves 60 miles west and 40 miles south.
Considering their starting point as the origin, we get two points A and B in the coordinate system, where A (the first plane's destination) is (50, 75) and B (the second plane's destination) is (-60, -40). The distance between A and B can be found using the distance formula:
d = √((x2-x1)² + (y2-y1)²)
d = √((-60-50)² + (-40-75)²)
d = √((-110)² + (-115)²)
d = √(12100 + 13225)
d = √(25325)
d ≈ 159 miles
Therefore, the correct answer is not listed among the choices provided. The distances offered for selection are not accurate based on the calculation. This suggests there may be a typo in the question or the given choices.