Problem Statement

Horizontal Versus Vertical Gap Between the Two Cyclists' Stopping Points Two cyclists, Rider P and Rider Q, are 500 km apart on a straight East-West highway. They start riding towards each other at the same time. Rider P starts from the West and moves East at a constant speed of 57 km/hr. Rider Q starts from the East and moves West at a constant speed of 40 km/hr. After exactly 1 hour of riding, Rider P takes a left turn, rides for another 40 minutes at the same speed, and stops at point M. Meanwhile, Rider Q rides straight for a total of 1.5 hours from the start, then takes a left turn, rides for 30 minutes at the same speed, and stops at point N. What is the absolute difference between the horizontal and vertical distances separating points M and N?