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The problem :

A spy climbs out of a submarine into a rubber boat 2 miles east of point P on a straight north-south shoreline. He wants to get to a house on the shore 6 miles north of P. He can row 3mi/h and walk 5 mi/h. He intends to row directly to a point north of P and then walk the rest of the way. How far north of P should he land in order to get to the house in the shortest possible time.

What I understood enter image description here

And I am trying to optimize $ f(x) = 6 - x + \sqrt{x^2 + 4} $, but when i get to the derivative, its discriminant is negative and I can't continue. I am not looking for a solution, but just tips on where I got the exercise wrong. Thank you!

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    $\begingroup$ You have not taken into account the rates at which he rows and walks. $\endgroup$ Commented Jul 2, 2016 at 8:25

1 Answer 1

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You should be trying to minimise

$$\frac{\sqrt{4+x^2}}{3}+\frac{6-x}{5}$$

because the time taken equals distance divided by speed.

So you just forgot to divide each distance by the speed.

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