about mechanics

Suppose Y to be the time taken for the rock to climb to its max. height
then,
(v-u)/Y = a , where v is the final velocity, u is the init. velocity, a is acceleration
=>(0-u)/Y = a , take a=-g m/s^2
=>Y = u/g seconds ....(1)

consider the formula, s = ut+(1/2)at^2
total displacement for the rock come back to the starting position is 0.
so,
=>0= ut+(1/2)at^2
=>(u-(1/2)gt)t =0
=>t=0 or t=2u/g
total time for the whole journey, t=2u/g ....(2)
compare (1)&(2),
therefore, Y=(1/2)t

If neglecting air resistance, then the answer is (1/2)t.

因為during rising and falling都是向下accelerating (due to gravity must pointing downwards!!).

If there is air resistance, then
向上既時間要少ｄ既.

因為both gravity & air resistance are resisting the stone moving upwards, so it will reach its highest position (lower than before) in a shorter time.