s = 3.6 t, t > 0
Let's calculate the length of Charlie's shadow as a function of how far Charlie is from the light pole. If you consider Charlie and his shadow to create a right triangle with the hypotenuse being from the tip of the shadow to the top of Charlie's head, you'll see that there's a similar right triangle with the light point, where the light pole is proportional to Charlie's height, the distance from the base of the light pole to the tip of the shadow corresponding to the length of Charlie's shadow, etc.
So if Charlie is n feet from the light pole, the following relationship holds
16/6 = (n+s)/s
Solving for s.
16/6 = (n+s)/s
16/6 = n/s+s/s = n/s + 1 = n/s + 6/6
10/6 = n/s
s * 10/6 = n
s = n / 10/6 = n * 6/10 = 0.6 n
So the length of Charlie's shadow is 0.6 ft for every foot Charlie is from the light pole. We know that Charlie is moving at the rate of 6 feet per second, so Charlie is 6t feet away from the light pole. So with this in mind, the desired expression is
s = 0.6 * (6 * t)
s = 3.6 t
So for any given time "t" where t > 0, the length of Charlie's shadow is 3.6 t.
