1. The problem statement, all variables and given/known data Two towns A and B, are situated directly opposite to each other on the banks of a river whose width is 8 miles and which flows at speed of 4 mi/hr. A man located at A wishes to reach town C which is 6 miles upstream from and on the same side of the river as town B. If his boat can travel at a maximum speed of 10 mi/hr and if he wishes to reach C in the shortest possible "time", what course must he follow and how long will the trip take? 2. Relevant equations (Not applicable) 3. The attempt at a solution Intuition tells me that the resultant velocity should be in the direction of AC for shortest possible time. I calculated for this case, and the result matches. But I cannot quite convince myself that the resultant velocity should be in the direction of AC for minimum time. It does not seem straight forward to me that the time will be minimum for the shortest (in terms of length) path. And that is because the magnitude of velocity can be higher for other trajectory than this shortest (in terms of length) path. I tried to use calculus of variation, but the equation becomes quite messy. Any suggestion will be appreciated.