Solving for t and h when both are unknown.

[BUConsul]

Okay, so this question has really gotten under my skin.

"An object falls a distance h from rest. If it travels 0.51h in the last 1.00 s, find (a) the time and (b) the height of its fall."

I have some groundwork laid out: a=-g, h=.5gt^2, and that between two points 1 second apart the average velocity is .51h(m/s). The only problem is I end up with equations that are in terms of unknowns 't' and 'h'. I know I lam probably missing something painfully obvious, and I'd appreciate any help I can get. Also, if it's not to much trouble, some hints versus the actual solution would be appreciated. (I'd like to do as much as possible, how else can I learn?)
Thanks in Advance - David

 

[gerben]

Divide the falling time in two, so that it takes t1 seconds to fall the first part and t2=1sec to fall the last part. Then you can give an expression for the velocity at the start of the last part use this combined with the acceleration to make a formula for the distance traveled during the last part and equate that formula with the known height (0.51h) that is traveled during the last part.