Answer:
11.97 ft/s
Step-by-step explanation:
Let x be the vertical distance of man from point P and y be the vertical distance of woman from point P
Total time=5+15 =20 mins
[tex]\frac{dx}{dt}=5 ft/s[/tex]
[tex]\frac{dy}{dt}=7 ft/s[/tex]
Distance traveled by man in 20 min
a=[tex]5\times 20\times 60=6000 ft[/tex]
1 min=60 s
Distance traveled by Woman in 15 min
[tex]b=7\times 15\times 60=6300 ft[/tex]
z=500 ft
x+y=6000+6300=6900 ft
[tex]d=\sqrt{(x+y)^2+(500)^2}[/tex]
Using Pythagoras formula
[tex]Hypotenuse=\sqrt{(base)^2+(Perpendicular\;side)^2}[/tex]
[tex]d=\sqrt{(6900)^2+(500)^2}=6918.09 ft[/tex]
[tex]d=6918.09 ft[/tex]
[tex](x+y)^2+(500)^2=d^2[/tex]
Differentiate w.r.t t
[tex]2(x+y)(\frac{dx}{dt}+\frac{dy}{dt})=2d\frac{d d}{dt}[/tex]
[tex]2(6900)(5+7)=2(6918.09)\frac{d d}{dt}[/tex]
[tex]2\times 12\times 6900=2(6918.09)\frac{d d}{dt}[/tex]
[tex]\frac{d d}{dt}=\frac{2\times 12\times 6900}{2(6918.09)}[/tex]
[tex]\frac{d d}{dt}=11.97 ft/s[/tex]
