- #1

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So far, I've figured out how to do this:

Let [tex]x[/tex] be the distance along the bank that he should land in order to get back as quickly as possible.

Since he's 50 m away from the bank, he has to swim a distance of [tex]\sqrt{x^2 + 50^2}[/tex] metres, and then run a distance of [tex]100-x[/tex] metres.

The total amount of time taken to do this is [tex]\frac{7}{100-x} + \frac{3}{\sqrt{x^2 + 50^2}}[/tex].

Now, I can tabulate everything on an Excel spreadsheet, and figure out the answer from there, which is: he should land roughly 23.7 metres along the bank from where he is. Is there a more elegant way of getting around this?