Answer:
[tex]\frac{d}{dt} (x+y)=\frac{15}{2} \frac{ft}{s}[/tex]
Step-by-step explanation:
If we see the file attached. The lamppost and the person form a triangle. The hight of the triangles are set by 10 ft from the lamppost and 6 ft from the person.
We also know that the person moves at a rate of 3 [tex]\frac{ft}{s}[/tex]
So, [tex]\frac{dx}{dt} =3\frac{ft}{s}[/tex]
As we have similar triangles:
[tex]\frac{6}{10} =\frac{y}{x+y}[/tex]
Solving the equation by y:
[tex]4y=6x[/tex]
[tex]y=\frac{3}{2}*x[/tex]
If we derivate the expression:
[tex]\frac{dy}{dt} =\frac{3}{2}\frac{dx}{dt}[/tex]
Knowing that [tex]\frac{dx}{dt} =3\frac{ft}{s}[/tex]
[tex]\frac{dy}{dt} =\frac{3}{2}*(3)=\frac{9}{2}[/tex]
[tex]\frac{d}{dt} (x+y)=\frac{dx}{dt}+\frac{dy}{dt}=3+\frac{9}{2} =\frac{15}{2} \frac{ft}{s}[/tex]
