Posted by Bernardo on Monday, October 24, 2011 at 10:09am.
A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?

calc related rates  Steve, Monday, October 24, 2011 at 11:54am
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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