Posted by **Joe** on Tuesday, April 3, 2012 at 5:47pm.

A street light is at the top of a 19 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 feet from the base of the pole?

- Calculus -
**Reiny**, Tuesday, April 3, 2012 at 6:21pm
Let her distance from the pole be x ft

let the length of her shadow by y ft

given: dx/dt = 7 ft/s

find: d(x+y)/dt when x = 30

by ratios:

19/(x+y) =6/y

19y = 6x+6y

13y = 6x

13dy/dt = 6dx/dt

dy/dt = 6(7)/13 = 42/13 ft/s

(notice dy/dt is a constant , which means the shadow is lengthening and moving at a rate independent of where she is)

d(x+y)/dt = 7 + 42/13 = 133/13 or appr 10.23 ft/s

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