Speed of moving shadow due to light source

[hqjb]

Homework Statement

A girl 5 feet tall is running at the rate of 12 feet/second and
passes under a street light 20 feet above the ground. Find how
rapidly the length of her shadow is increasing when she is 20
feet past the base of the street light.

The Attempt at a Solution

I let the distance of girl from light be S = 12t
I let the distance of shadow from light be X,

Due to similar triangle,

$\frac{x}{x-12t} = \frac{20}{5}$

$-15x=-240t$

$x=16t$

$\frac{dx}{dt}=16$

But the ans is 4ft/sec any clues as to where I went wrong?

 

[BruceW]

The problem does not want dx/dt. Because x is not the length of her shadow. x is the length of her shadow plus her distance from the base of the street light.

 

[hqjb]

The problem does not want dx/dt. Because x is not the length of her shadow. x is the length of her shadow plus her distance from the base of the street light.

Ah...semantics. Thanks. So I suppose that if they were looking for the speed for the tip of the shadow then that would be the right answer?

 

[BruceW]

Yes. Your answer of 16 ft/second is the speed of the tip of the shadow. The rate of change of the length of the shadow is different to this because the other end of the shadow (at the girl) is also moving.