Four paths concepts? (Calc-based Physics 1)

I'm having trouble with this physics problem. I have no idea where to start.

The labeled graphs below represent the upward trajectories of 4 bodies, two sliding upwards on frictionless inclines and two in free flight. Note that all 4 bodies reach the same maximum height (9 meters) after traveling from the same initial elevation (0 m).

http://i.imgur.com/6g12l.png

Answer choices (greater than, less than, equal to)
• The time of travel of Q is ___ that of P
• The initial speed of P is ___ that of Q.
• The initial speed of N is ___ that of R.
• The time of travel of N is ___ that of R
• The initial speed of Q is ___ that of N.
• The time of travel of N is ___ that of Q.

Any ideas? Thanks a ton.

A similar question was recently asked in:
http://answers.yahoo.com/question/index;…
- but not answered!
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Before starting, there are some simple observations and deductions to make:

As the graphs are of y vs. x, each simply shows the shape of the path followed by each body.
P is sliding up a steep incline and Q is sliding up a less steep incline.
N and R follow parabolic trajectories - i.e they are simple projectiles.

P and Q must each start with a the same kinetic energy as they have zero kinetic energy at 9m. All of their KE is turned to PE.

N and R are must have equal vertical components of initial velocity to reach the same height. They will reach 9m after the same times, as the vertical motion of projectiles with the same initial vertical components of velocity are identical. However R has a bigger horizontal component of velocity than N - so R travels further in the time needed to reach max height.
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There are different ways to explain these - all of them are messy to put into words, but I'll try. I'm assuming you are familiar with kinematics, projectiles and of conservation of mechanical energy.