Question: A man stands at a point \(A\) on the bank of a straight river, \(1 \mathrm{~km}\) wide, which is flowing at speed of \(12 \mathrm{~km} / \mathrm{h}\). To reach point \(\mathrm{B}, 10 \mathrm{~km}\) down the river on the opposite bank, he first rows his boat to a point \(\mathrm{P}\) on the opposite bank and then walks the remaining distance to \(\mathrm{B}\) as shown below. He can row at a speed of \(3 \mathrm{~km} / \mathrm{h}\) (in still water) and he walks at \(6 \mathrm{~km} / \mathrm{h}\).

Determine the angle \(\theta\) that the man's heading (direction in which he rows) should make with a perpendicular to the river so that he will reach B in the shortest possible time. What distance will the man walk in this case?

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