Step 1 :Let's denote the speed of the boat in still water as b (km/h) and the speed of the current as c (km/h).
Step 2 :When the boat is going upstream (against the current), its speed is (b - c) km/h. When it is going downstream (with the current), its speed is (b + c) km/h.
Step 3 :We know that speed is distance divided by time. So, we can set up two equations based on the information given in the problem: \(4(b - c) = 128\) and \(2(b + c) = 128\).
Step 4 :Solving these equations simultaneously, we find that b = 48 and c = 16.
Step 5 :Final Answer: The rate of the boat in still water is \(\boxed{48 \frac{\mathrm{km}}{\mathrm{h}}}\) and the rate of the current is \(\boxed{16 \frac{\mathrm{km}}{\mathrm{h}}}\).