Rate of a growing shadow

MediumCalculus~5m

A $6$ -foot-tall person walks away from a lamp post at $40$ feet per minute. When they are $10$ feet from the post, their shadow is $15$ feet long. How fast is the length of the shadow increasing (in feet per minute) when they are $40$ feet from the post?

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Similar triangles: $\dfrac{H}{x+s}=\dfrac{6}{s}$ . Use $x=10,s=15$ to find the lamp height $H$ .
You'll get $s=\tfrac32 x$ , so $ds/dt=\tfrac32\,dx/dt$ - constant, independent of position.

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Rate of a growing shadow

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