Distance between P and Q = 60 km (Q is to the west of P). Distance between P and R = 80 km (R is to the south of P).

Step 1: Place P as the origin point $(0, 0)$ in a coordinate plane. Q lies to the west of P, so Q can be represented at $(-60, 0)$. R lies to the south of P, so R can be represented at $(0, -80)$.

Step 2: Since we have a right-angled triangle, where PQ is horizontal (west) and PR is vertical (south), the distance between Q and R is the hypotenuse (QR).

The Pythagorean Theorem formula is: $QR^2 = PQ^2 + PR^2$

Substitute the given values: $QR^2 = 60^2 + 80^2$ $QR^2 = 3600 + 6400$

Take the square root of both sides: $QR = 100$

The distance between Q and R is 100 km