If he ignores the current and just swims across the river letting the current carry him downstream, his movement looks like this:
This time the resultant vector is the hypotenuse, but we don't need to find it as the only things we are interested in are the time it takes to go the 15 meters across the river and how far downriver the swimmer ends up. First we find the time it takes to get across.
Since the swimmer is in the water for 10.0s, he is carried downriver the whole time at the constant velocity of the current. He will end up:
10 meters downriver, but he will have crossed the river faster.