parametric equations

Two particles are moving in the plane. For t > 0, Particle One has parametric equations:

(x₁(t), y₁(t) ) = (t,tA????1ln(t))

For t > 0, Particle Two has parametric equations

(x₂(t),y₂(t)) = (t, t^t)

(a)The tangent lines to the particles are parallel at two times. Find these times.  
(b) At the first time the tangent lines are parallel, at what rate is the distance between the two particles changing?  
(c) At the second time the tangent lines are parallel, at what rate is the distance between the two particles changing?  
(d) For particle One, when is the tangential direction is parallel to the x-axis at time t?  
(e) What's the speed of particle One given by the formula s(t)?
(f) What's the formula of the rate of change of the speed of particle One?