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I've been trying to solve this problem for hours but I still can't seem to get the right answer.

The question is,

Hieu can row a boat across a circular lake of radius 2 km at 3 km/h. He can walk around the edge of the lake at 5km/h.
What is the longest possible time Hieu could take to get from P to R by rowing from P to Q and then walking from Q to R?

I've attached a picture of the question so that it's easier to visualize the problem.

So far I've found that PQ is (4/3) cos (theta) and QR is (pi)(theta)/225.

I've done this by using basic sine trig function to find PQ and getting the circumference of QR. I took the derivative of the PQ +QR and got an answer that is too small. I suspect that I've gotten the (theta) of QR wrong. For QR, my (theta) is 2(theta)

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(Original post by tdot333)
So far I've found that PQ is (4/3) cos (theta) and QR is (pi)(theta)/225.
I think you may be mixing your units.

If you've differentiated cos to get -sin, without multiplying by anything else, then that's assumed that theta is in radians, but the second part, QR, clearly has theta in degrees.

I would do it all in radians myself.

PS: This is "Sixth form" rather than "Undergraduate" as it's from a book aimed at prep for the IB.
Last edited by ghostwalker; 11-07-2012 at 20:56.