Dick takes twice as long as Jane to run any given distance. Starting at the same moment, Dick and Jane run towards each other from opposite ends of the schoolyard, a total distance of x, at their respective constant rates until they meet.
Compare Quantity A and Quantity B
- Quantity A = The fraction of the total distance x that is covered by Jane
- Quantity B = 2x/3
According to me Quantity A = 2/3. => A and B cannot be compared because:
1) when x<1 => A is greater
2) when x=1 => A = B
3) when x>1 => B is greater
However as per the answer key: A = B.
Edit: 
For any length of time, Jane will always run twice as far as Dick. However, their distances combined is always $x$. We can set up a system of equations for $D$, the distance Dick runs, and $J$, the distance Jane runs. $$D+J=x$$ $$D=\frac{J}{2}$$ Thus $$J+\frac{J}{2}=x$$ Therefore $J=\frac{2x}{3}$.