A river is \(104\) metres wide and the current flows at \(0.5\text{ m s}^{-1}\) parallel to its banks. A woman can swim at \(1.6\text{ m s}^{-1}\) in still water. She swims from point \(A\) and aims for point \(B\), which is directly opposite, but she is carried downstream to point \(C\). Calculate the time it takes the woman to swim across the river and the distance downstream, \(BC\), that she travels.