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1. The problem statement, all variables and given/known data

I am stuck somewhere on a related rates problem, i think that i am missing something rather obvious, but i cannot figure out so far.

-A street light is mounted at the top of the 15 ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole.

2. Relevant equations

3. The attempt at a solution

Here it is what i did so far. I drew a triangle to describe the situation, i let one side of the triangle be 15 ft, i let x be the distance from the pole to the man, and i let y be the length of the shadow of the man. Then from the similarity of the triangles i got this relationship

[tex]\frac{15}{x+y}=\frac{6}{y}[/tex] i tried to rearrange this a little and i came up with

[tex]y=\frac{2}{3}x[/tex]

From the data i also know that [tex]\frac{dx}{dt}=5[/tex]

I also know that i should let [tex]x=40[/tex] after i come up with a relationship between the rate at which the man is moving and the rate of change of the tip of his shadow.

Here it is where i am stuck, for if we just implicitly differentiate [tex]y=\frac{2}{3}x[/tex] with respect to time it does not work. What am i missing here??

Any help would be really appreciated!!

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# Homework Help: Need help! Related rates

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