Posted by **AH** on Friday, November 2, 2012 at 1:06pm.

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 7 ft/s along a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole?

- Math -
**Reiny**, Friday, November 2, 2012 at 5:23pm
make a sketch

label the man's distance from the post as x

and the length of his shadow y

by similar triangles and ratios

6/y = 15/(x+y)

15y = 6x + 6y

9y = 6x

3y = 2x

3dy/dt = 2dx/dt

dy/dt = (2/3)(7) = 14/3 ft/s

so the length of his shadow is **lengthening** at 14/3 ft/s

but it is **moving** at 14/3 + 7 or 35/7 ft/sec

- Math -
**AH**, Saturday, November 3, 2012 at 1:12am
Thank you very much!

By the way, 14/3+7 equals 35/3, not 35/7.

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