Optimization..help please!
A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 4 miles per hour and can walk 5 miles per hour, where should the boat be landed in order to arrive at a town 7 miles down the shore from P in the least time?

Question

Optimization..help please!
A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 4 miles per hour and can walk 5 miles per hour, where should the boat be landed in order to arrive at a town 7 miles down the shore from P in the least time?

aum · Answer

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aum · Answer

Rows the boat along IB and walks along BQ.
Time taken = IB / 4  +  BQ / 5 = sqrt(4^2 + x^2) / 4 + (7 - x) / 5

Find the minimum time.

anonymous · Answer

Thank you so much! I really appreciate your help. That being said, the question is asking for the point on the beach exactly she should row to. I'm guessing that would be the coordinate where B intersects PQ but I am not sure how to find that point

aum · Answer

"where should the boat be landed in order to arrive at a town 7 miles down the shore FROM P".

Just find x and saw she should land the boat x miles from P.  (put the number you find the in place of x)