MHB 2.6.284 AP calculus Exam Lamp and Shadow related rates

[karush]

yes I know this is a very common problem but likewise many ways to solve it
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ok I really have a hard time with these took me 2 hours to do this
looked at some examples but some had 3 variables and 10 steps
confusing to get the ratios set up... ok my take on it is here

see if you can solve it under 5 min

Spoiler

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[skeeter]

given $\dfrac{dx}{dt}= 4 \text{ ft/sec}$

Spoiler

$\dfrac{15}{x+s} = \dfrac{6}{s} \implies s = \dfrac{2x}{3} \implies \dfrac{ds}{dt} = \dfrac{2}{3} \cdot \dfrac{dx}{dt} = \dfrac{8}{3} \text{ ft/sec}$