If the distance the first car travels north in time t is a, then a=40t. Similarly the second car travels b=30t.
Their straight line distance apart after time t is given by Pythagoras’ Theorem:
z=√(a²+b²)=√(40t)²+(30t)²)=50t.
a) The rate they are separating is dz/dt=50, so they are separating at a constant rate of 50mph. In other words, this is the square root of the sum of the squares of their speeds.
b) The rate is independent of time and so after 2 hours their rate of change is still 50mph.