This problem can only be done under the basic assumption that the water velocity is constant, but the downstream direction is opposite.

So let the distance be d, the downstream speed be d/A, the upstream speed be d/B, and the water flow speed be equal to v=(d/A-d/B)/2.

So the drift time is equal to d/v = 2/(1/a-1/b) = 2ab/(b-a).