The word problem goes like this:
It takes some people 2 hours to row up a river (6,4 km long) and back again (so total distance travelled = 12,8 km). The current is 2,4 km/h. How fast would the boat have travelled if there were no current?
I reason like this: When there is a current, the speed is 6,4 km/h. When the boat travels upstream, the current slows the boat down by 2,4 km/h, and when the boat travels downstream the current speeds up the boat equally much. So the current cancels itself out and the speed is still 6,4 km/h. But that's not the correct answer, the correct answer is 7,2 km/h.
Drawing a picture of the problem and assigning variable names doesn't help me very much, it's just a line with length L = 6,4 units long, a boat with the constant speed x and the current represented by an arrow.
It seems to me that the correct answer is an equation system, one linear equation for the way up and another for the way down, with two variables (time and speed). But that seems a bit too complicated. What am I thinking wrong? Thank you for any help!