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

A man with a boat is located at point P on the shore of a circular lake of radius 5 miles. He wants to reach the point Q on the shore diametrically opposed to P as quickly as possible. He plans to paddle his boat at an angle t(0<t<pi/2)<or equal to** to PQ to some point R on the shore, then walk along the shore to his Q. If he can paddle 3.4 miles per hour and walk at 3.8 miles per hour, what is the shortest possible time it will take him to reachQ?

2. Relevant equations

3. The attempt at a solution

I've got one part of the problem, and I understand the concept of optimization, but how would i find the length of the paddle distance?

((t*10pi)/(2pi)) this is what i came up with to find the length of his walking distance. then divide that by 3.8 and divide whatever his paddle distance is by 3.4 to have total time. If I have the formula, I can easily differentiate it, so no need to do any of that.

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# Circle optimization

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