A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at a rate of 4 feet per second. If the height of a streetlight is 15 feet, what is the rate at which a person's shadow is lengthening?

Question

Lyric Wood

Mathematics

3 November, 17:52

A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at a rate of 4 feet per second. If the height of a streetlight is 15 feet, what is the rate at which a person's shadow is lengthening?

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Answers (1)

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Elsie Oneal · Answer 1

Let the distance from the pole be x and the length of the shadow be s. Using the law of similar triangles, we have:

s/6 = (x+s) / 15

thus

5s=2x+2s

3s=2x

hence

ds/dt=2/3 dx/dt

but

dx/dt=4 ft per second

hence

ds/dt=2/3*4=8/3