(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A rower in a boat at a point P, 3km from the closest point Q on a straight shorline, wishes to reach a point r which is 5 km along the shoreline from Q. If he can row at 2km/h and walk at 4km/h along the shoreline, how far from point Q should the rower land the boat in order that the total time for the trip PR is minimized.

3. The attempt at a solution

Okay so if I let x be the distance from point Q, then the equation should be:

t = 2(x^2+9)^(1/2) + 4(5-x)

right?

Then

dt/dx = 2x/(x^2+9)^(1/2) - 4

0 = 2x/(x^2+9)^(1/2) - 4

4(x^2+9)^(1/2) = 2x

(x^2+9)^(1/2) = 1/2x

x^2+9 = 1/4x^2

but that gives no solution.

Could someone point me to where I went wrong please?

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# Min/max problem

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