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# Calc Help

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Eric and Harrison are standing in a field, and Eric is 400 feet directly East of Harrison. Eric starts to walk North at a rate of 4 feet per second, while Harrsion starts to walk South at the same time at a rate of 6 feet per second. After 30 seconds, at what rate is the distance between Eric and Harrison changing?

Jun 15, 2018

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We can model the rate of a change as a right triangle with base $$x = 400$$ feet and height y increasing at a rate of 10 feet per second.

After 30 seconds, $$y=10\cdot30=300$$

If the distance between Eric and Harrison is z, the Pythagorean Theorem gives us: $$z^2 = x^2 + y^2$$.

The distance between Eric and Harrison is: $$x^2=300^2+400^2\Rightarrow x=500$$

Differentiating both sides also yields $$2z · z' = 2x · x' + 2y · y'$$. Plugging in our values, we get $$2 · 500z' = 2 · 400 · 0 + 2 · 300 · 10$$, which gives us $$z' = 6$$ feet per second.

I hope this helped,

Gavin

Jun 15, 2018