Answer:
a. [tex]\frac{dx}{dt}=20ft/s[/tex]
b. [tex]\frac{d(x+L)}{dt}==25ft/s[/tex]
Explanation:
Using the triangle theorem both triangle the woman makes between the light so the rate of change of length can use geometry first
[tex]tan(\beta)=\frac{24ft}{L+x}=\frac{6ft}{x}[/tex]
Solve to find the rate relation
[tex]x=\frac{24}{6}*L[/tex]
[tex]x=4*L[/tex]
Now the rate of the change rate
[tex]\frac{dx}{dt}=4*\frac{dL}{dt}[/tex]
[tex]\frac{dx}{dt}=4*5ft/s=20ft/s[/tex]
Finally the rate of her shadow moving
[tex]\frac{d(x+L)}{dt}=\frac{dx}{dt}+\frac{dL}{dt}[/tex]
[tex]\frac{d(x+L)}{dt}=20ft/s+5ft/s=25ft/s[/tex]
