A motorboat takes 4 hours to travel 128 kilometers going upstream. The return trip takes 2 hours going downstream. What. is the rate of the boat in still water and what is the rate of the current?
Note that the ALEKS graphing calculator can be used to make computations easier.
Rate of the boat in still water:
$\square \frac{\mathrm{km}}{\mathrm{h}}$

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 \(\boxed{16 \frac{\mathrm{km}}{\mathrm{h}}}\).