, 2022

Because the two women cross the river in the same amount of time, the north-south components of their velocities are the same value $y$. The east-west components of Melanie's and Sherry's velocities must be values $-x$ and $x$, respectively, because the two women meet halfway between their starting points. But Melanie is swimming against the river's current, and Sherry is swimming with the river's current, so relative to the water, Melanie's velocity is given by the vector $\langle -x - 14, y \rangle$, and Sherry's velocity is given by the vector $\langle x - 14, y \rangle$. Thus the squares of their speeds are
$$80^2 = (x + 14)^2 + y^2 = x^2 + 28x + 196 + y^2 \text{ and}$$
$$60^2 = (x - 14)^2 + y^2 = x^2 - 28x + 196 + y^2.$$
Subtracting and solving for $x$ yields $x = 50$, from which $y = 48$. It takes each woman $\frac{264}{48} = \frac{11}{2}$ minutes to complete her swim. Each woman swims along the river a distance of $50 \cdot \frac{11}{2} = 275$ meters, so $D = 2 \cdot 275 = 550$.