A man 6 feet talk walks at a rate of 5 per second toward a street light that is 16 feet tall. At what rate is the length of his shadow changing when he is 10 feet from the base of the light?

Question

A man 6 feet talk walks at a rate of 5 per second toward a street light that is 16 feet tall.  At what rate is the length of his shadow changing when he is 10 feet from the base of the light?

anonymous · Answer

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$x$ is the length of the man's shadow, $h$ is the distance between the man and the light. You're given that $\dfrac{dh}{dt}=-5$ (-5 because $h$ is decreasing), and you have to find $\dfrac{dx}{dt}$.

Similar triangles give the ratio,
$$\frac{6}{x}=\frac{16}{x+h}$$