Hello,

T=T1+T2 is still a uniform distribution (I'll let you think over which interval).

Then T3=T+G, where G follows a geometric distribution (because it will give the time you get a taxi)

So T3-T ~ G(1/2)

First condition with respect to T and find the pdf of T3|T.

Then use this formula : and .

Looks a bit complicated, but not that much.