Answer: As depicted in the diagram, APQC represents the path taken by the guy through the sand, the time it took him to get from A to C, and the distance travelled by him.
![\[\begin{aligned} &T_{\text {sand }}=\frac{A P+Q C}{1}+\frac{P Q}{v} \\ &=50 \sqrt{2}(1 / v+1) \end{aligned}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8886dbc11289311d15754f200ed136d0_l3.png "Rendered by QuickLaTeX.com")
The shortest distance will be ARC from the diagram.
![\[\begin{aligned} &T_{\text {outside }}=A R+R C / 1 s \\ &A R=\sqrt{75^{2}+25^{2}} \\ &R C=A R=25 \sqrt{10} s \\ &T_{\text {sand }}<T_{\text {outside }} \\ &V>0.81 m / s \end{aligned}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5454ca1e31f1dbea9eaca59622cec3d9_l3.png "Rendered by QuickLaTeX.com")
A man wants to reach from A to the opposite comer of the square C. The sides of the square are 100 m. A central square of 50 m × 50 m is filled with sand. Outside this square, he can walk at a speed 1 m/s. In the central square, he walk only at a speed of v m/s. What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand?
A man wants to reach from A to the opposite comer of the square C. The sides of the square are 100 m. A central square of 50 m × 50 m is filled with sand. Outside this square, he can walk at a speed 1 m/s. In the central square, he walk only at a speed of v m/s. What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand?