Answer:t=2.11 hr
Step-by-step explanation:
Given
Aydlett is 2 miles offshore and village is 6 miles down a straight line from the Point on the shore nearest the island
Person can row boat at 2 mph in water and can walk 5 mph in land
Let us suppose Person land the boat at a x miles  from Point on the shore
thus time taken by him to reach
[tex]t_1=\frac{\sqrt{x^2+2^2}}{2}[/tex]
Time taken person to reach village by land is
[tex]t_2=\frac{6-x}{5}[/tex]
total time[tex]=\frac{\sqrt{x^2+2^2}}{2}+\frac{6-x}{5}[/tex]
we need the time to be least so differentiate t w.r.t to x
[tex]\frac{\mathrm{d} t}{\mathrm{d} x}=\frac{2x}{2\cdot 2\cdot \sqrt{4+x^2}}-\frac{1}{5}[/tex]
Equating Above term to zero to get minimum time
[tex]\frac{x}{2\sqrt{4+x^2}}=\frac{1}{5}[/tex]
[tex]25x^2=16+4x^2[/tex]
[tex]x=\frac{4}{\sqrt{21}}[/tex]
Substituting x in time equation
[tex]t=\frac{\sqrt{4+0.761}}{2}+\frac{6-0.872}{5}[/tex]
[tex]t=2.116 hr[/tex]
