What have you tried?
I assume that you know the kinematic equations.
For each of the particles you are given the initial position
Their initial velocity and their acceleration .
Hint: for simplicity since Z is arbitrary and you are only care about distance from z you might as well put the origin of your coordinate system at z and so .
Now write out each of the kinematic equations you will get a system of 2 equations in x and t.
What ideas have you gotten so far?
[EDIT] I'll leave you in TheEmptySet's capable hands.
fixed it now