Answer
See explanation
Work Step by Step
Let $t_x$ be the time elapsed in going and $t_y$ be the time elapsed in returning.
Using the speed equation $v=\frac{s}{t}$:
$$50=\frac{2(100)}{t_x+t_y}$$
$$t_x+t_y=\frac{200}{50}$$
$$t_x+t_y=4$$
$$x=\frac{100}{t_x}$$
$$t_x=\frac{100}{x}$$
$$y=\frac{100}{t_y}$$
$$t_y=\frac{100}{y}$$
Substituting $t_x$ and $t_y$:
$$\frac{100}{x}+\frac{100}{y}=4$$
$$\frac{100y+100x}{xy}=4$$
$$\frac{100y}{4}+\frac{100x}{4}=xy$$
$$25y+25x=xy$$
$$25y-xy=-25x$$
$$y(25-x)=-25x$$
$$y=\frac{-25x}{25-x}$$
$$y=\frac{25x}{x-25}$$
