- #1

QuarkCharmer

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## Homework Statement

Stewart Calculus 6E, 3.8 #14

At noon, ship A is 150km west of ship B. Ship A is sailing east at 35km/h, and ship B is sailing north at 25km/h. How fast is the distance between the ships changing at 4pm?

## Homework Equations

Distance Formula I think.

## The Attempt at a Solution

Again, I am having trouble phrasing the question. It seems to me, that I need to find an equation in terms of distance and then implicitly differentiate. If the coordinate points of the ships are A(0,0) and B(150,0) at time 12, I thought that I could solve for the distance like this.

[tex]D = \sqrt{\Delta X^2+\Delta Y^2}[/tex]

Since, I am looking for D', I would differentiate that to be:

[tex]D' = 1/2(\Delta X^2+\Delta Y^2)^{\frac{-1}{2}}\frac{d}{dt}(\Delta X^2+\Delta Y^2)[/tex]

[tex]D' = 1/2(\Delta X^2+\Delta Y^2)^{\frac{-1}{2}}(2 \Delta X \Delta X'+2 \Delta Y \Delta Y')[/tex]

...and that is where I realized that I am going about this all wrong.