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[jesusdiwa15]

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VI. An island is at point A, 4 km offshore from the nearest point B on a straight beach. A woman on the island A wishes to go to a point C, 6 km down the beach from B. She can go by rowboat at 5 kph to a point P between B and C, and then walk at 8 kph along a straight path from P to C. To what point should she row in order to reach his destination in the least time (distance of point P from point B)? (16 points)

Thanks

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[Deleted member 4993]

VI. An island is at point A, 4 km offshore from the nearest point B on a straight beach. A woman on the island A wishes to go to a point C, 6 km down the beach from B. She can go by rowboat at 5 kph to a point P between B and C, and then walk at 8 kph along a straight path from P to C. To what point should she row in order to reach his destination in the least time (distance of point P from point B)? (16 points)

Thanks

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[stapel]

VI. An island is at point A, 4 km offshore from the nearest point B on a straight beach. A woman on the island A wishes to go to a point C, 6 km down the beach from B. She can go by rowboat at 5 kph to a point P between B and C, and then walk at 8 kph along a straight path from P to C. To what point should she row in order to reach his destination in the least time (distance of point P from point B)?

I'm assuming that the "his" in the last sentence is a typo, from when the exercise was converted from the so-called "sexist" "he" to "she".

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

For instance, you drew the diagram out on your paper, continuing the "beach" line from C to P the rest of the way to B. You noted that ABP is a right triangle. You noted that they're strongly hinting that they're wanting you to find the distance between P and B, so you label this part of the beach as, let's say, "x". You used the fact that ABP is a right triangle to create an equation relating x, 4, and the rowing distance AP. You created an expression, in terms of x, for the distance AP.

Then you created a time expression, using the fact that the walking distance will be 6 - x. Knowing that you're trying to minimize the time, you differentiated, and... then what?

Please be complete. Thank you!