1. The problem statement, all variables and given/known data Two boys can each paddle their kayaks at the same speed in still water. They paddle across a river which is flowing at a velocity of vR. Boy A aims upstream at such an angle that he actually travels at right angles to vR. Boy B aims at right angles to the bank, but is carried downstream. Which boy crosses the river in less time? 2. Relevant equations Cosine law: a2 = b2 + c2 - 2bccosA Sine law: a/sinA = b/sinB = c/sinC velocity = distance/time 3. The attempt at a solution I first drew a vector diagram. It consists of two right-angled triangles with a common leg. The hypotenuse of the first is the velocity of boy B and the hypotenuse of the second is the hypothetical path that boy A would travel without current. The shared leg is both the velocity of boy A and the hypothetical path that boy B would travel without current. The other two legs are both vR. Here I got confused: vB > vA, but isn't boy B's distance also greater than boy A's? I emailed my teacher for help and he gave me this terse answer: "Draw vector diagrams for boat A and boat B. Determine which boat has the larger component to it's course in the direction perpendicular to the bank. It will make it across first." But they have the same component to their course perpendicular to the bank, don't they? I don't understand what I'm missing. Could someone please help me?