A man wishes to cross a river of width \( 120 \mathrm{~m} \) by a motorboat. His rowing speed in...

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A man wishes to cross a river of width \( 120 \mathrm{~m} \) by a motorboat. His rowing speed in still water is \( 3 \mathrm{~m} / \mathrm{s} \) and his maximum walking speed is \( 1 \mathrm{~m} / \mathrm{s} \). The river flows with velocity of \( 4 \mathrm{~m} / \mathrm{s} \).
(a) Find the path which he should take to get to the point directly opposite to his starting point in the shortest time.
(b) Also, find the time which he takes to reach his destination.
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