# Homework Help: Optimization problem

1. Nov 26, 2007

### chompysj

1. The problem statement, all variables and given/known data

2. Relevant equations

a^2 + b^2 = c^2
A= (1/2)bh

3. The attempt at a solution

1)I labeled the distance traveled on the ocean as y and the distance traveled on land as x.

2)This one's kinda hard to describe: you know how the 100 yd distance and the shoreline form a triangle? I labeled the bottom of that triangle as w.

3) Pythagorean theorem:

100^2 + w^2 = y^2
(300-w)^2 + 65^2 = x^2

Area of triangle:

(300)(65) - (1/2)(300-w)(65) = 65w + (1/2)(65)(300-w)

Also, the derivatives:

dy/dt = 70 yd/min
dx/dt = 120 yd/min

This is kind of where I'm stuck. Am I on the right track with the whole w thing? Or am I headed in a completely wrong direction? Please help!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 27, 2007

### HallsofIvy

Okay, so "w" is the distance from the left at which the man lands on the shore.

Area of triangle? What in the world does area have to do with anything?

"Area" has nothing to do with this problem. If he goes distance y yds at 70 yd/min, how long does it take him? If he goes distance x yds at 120 yd/min, how long does it take him? What is the total time? Now use your formula to put everything in terms of your original variable, w. For what value of w is that time a minimum?

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