A man launches his boat from pointAon a bank of a straight river, 1 km wide, and wants to reach pointB, 1 km downstream on the opposite bank, as quickly as possible. He could row his boat directly across the river to pointCand then run toB, or he could row directly toB, or he could row to some pointDbetweenBandCand then run toB. If he can row 6 km/h and run 8 km/h,where should he land to reach? (We assume that the speed of the water is negligible compared to the speed at which the man rows.)Bas soon as possible

db=$\displaystyle 1-x$

ad=$\displaystyle \sqrt (x^2 +1)$

$\displaystyle \frac{\sqrt (x^2 +1)}{6}$= $\displaystyle \frac{1-x}{8}$

derivative:

$\displaystyle \frac{(x)}{6\sqrt (x^2 +1)}$= $\displaystyle \frac{1}{8}$

$\displaystyle 8x$= $\displaystyle 6\sqrt (x^2 +1)$

$\displaystyle 64x^2=36(x^2+1)$

$\displaystyle 64x^2=36x^2+36$

$\displaystyle 28x^2=36$

$\displaystyle x=\sqrt(36/28)$=1.1 km

t(0)=1.5 and t(8)=1.2..., so this should be the min, but it was marked wrong.