A boat crosses a straight river of width \(D\) that flows with a constant, uniform speed \(u\) parallel to its banks. The boat maintains a constant speed \(v\) relative to the water, where \(v < u\). To minimize the total downstream drift distance \(\Delta x\), the boat steers at an angle \(\theta\) upstream relative to the line perpendicular to the bank, resulting in a minimum drift distance of
\[\Delta x_{\text{min}} = D\sqrt{\left(\dfrac{u}{v}\right)^2 - 1}\]
In the limit as the boat's speed approaches the river's speed from below (\(v \to u^{-}\)), which of the following correctly describes the minimum downstream drift distance and the time required to cross the river?