If g > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z,...

Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have g-x=2t. So y-x=-t, y-g=-3t. ---> (y - x)/(y - g) = 1/3.
The answer is (B).