Question 763171
Let the distance between them be 150 after x hours.

In x hours, car travelling west covers 45*x miles
In x hours, car travelling south covers 55*x miles

Since they are travelling west and south which are perpendicular to each other,
the paths of the 2 cars and the distance between them, form a right triangle.

Two sides are 45*x an 55*x, and the hypotenuse is 150 miles.

Applying Pythagoras theorem,

(45*x)^2 + (55*x)^2 = 150^2

5050*x^2 = 22500

x^2 = 22500/5050 = 4.4554

{{{highlight(x = 2.11)}}} hours approximately

:)