Let us assume,
The velocity with which the elevatar ascends be u', the height attained by elevatar at time,T1 be h .
Thus,
u' = \(\frac{h}{T_1}\)
Equation of motion,
h = -u'T2 + \(\frac{1}{2}gT_2^2\)
∵ u' = \(\frac{h}{T_1}\)
h + \(\frac{h}{T_1}\)T2 = \(\frac{1}{2}gT_2^2\)
h(1 + \(\frac{T_2}{T_1}\)) = \(\frac{1}{2}gT_2^2\)
h = \(\frac{1}{2}\)\(\frac{gT_2^2}{(1+\frac{T_2}{T_1})}\)