Posted by **Nikki** on Sunday, September 5, 2010 at 12:56pm.

Jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline from the point nearest the boat. She can row 2mph and can walk 5mph. Where should she land her boat to reach the village in the least amount of time?

I'm totally stumped by this question. So far I have the picture of the problem, and that's about it. Help please?!

Thank you

- Math -
**Reiny**, Sunday, September 5, 2010 at 2:56pm
This is a good Calculus question.

label your diagram as follows

A - position of boat

B - point on shore closest to A

C- point on shore where he should row to (our answer)

V - position of the village

Clearly ABC is a right angle,

let BC = x, then CV = 6-x

AB = 2

AC = √(x^2 + 4)

Time in water = √(x^2 + 4)/2

time along shore = (6-x)/5

Time = (1/2)(x^2 + 4)^(1/2) + 6/5 - x/5

dTime/dx = (1/4)(x^2+4)^(-1/2)(2x) - 1/5

set this equal to zero and solve for x

let me know what you got.

- Math -
**Anonymous**, Tuesday, July 1, 2014 at 1:13pm
4/sqrt(21)? or 0.87287

## Answer this Question

## Related Questions

- math - a man is in a boat 2 miles from the nearest point on the coast. He is to...
- calculus - A man launches his boat from point A on a bank of a straight river, 3...
- Calculus 1 - A woman at a point A on the shore of a circular lake with radius r=...
- Calculus - You are in a boat "a" miles from the nearest point on the coast. You ...
- Calculus - A small island is 2 km off shore in a large lake .A woman on the ...
- Calculus Minima Problems - A small island is 2 km off shore in a large lake .A ...
- Calculus - A man is in a boat 4 miles off a straight coast. He wants to reach a ...
- calculus - A lighthouse is built on an exposed reef, 5.5 miles off-shore. The ...
- calculus - A lighthouse is built on an exposed reef, 5.5 miles off-shore. The ...
- math - Fadi is in a boat 3 kilometers away from the nearest point A at the sea ...