Solving Optimization Problem Homework

[chompysj]

Homework Statement

Homework Equations

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

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!

 

[HallsofIvy]

Homework Statement

Homework Equations

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

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.

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

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)

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

so, 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!

"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?