The physics
A packet let go from a moving balloon starts with the balloon's velocity. From a rising balloon, the packet goes up first. Then it falls.
After that only gravity acts. Take up as + and use one equation for the whole flight.
y = h + u t − ½ g t² v = u − g t v² = u² − 2g (y − h)
It lands when y = 0. Pick the positive root of the quadratic.
A ball passes every height below its top twice. With no air the flight is symmetric. The top is halfway between the two passes, and h = ½ g t₁ t₂.
A steady air drag f makes the two legs differ. Going up, a = g + f/m. Coming down, a = g − f/m. So the way down takes longer.