Posted by Bernardo on Monday, October 24, 2011 at 10:09am.
Draw a triangle.
If the woman is x feet from the pole, and her shadow extends an additional y feet,
18/(x+y) = 6/y
18y = 6(x+y)
18x = 6x + 6y
12x = 6y
2x = y
2 dx/dt = dy/dt
2(6) = dy/dt
Now, the distance of the shadow tip from the pole is x+y, so its speed is dx/dt + dy/dt = 6+12 = 18 ft/sec, regardless of the distance.
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