Swept Below the Put-In

A kayaker's upstream position (in km) evolves as $X_t = t + W_t$, where $W_t$ is a standard Brownian motion: steady paddling gains 1 km per hour of drift, while turbulence contributes unit-volatility Brownian noise. She launches at $X_0 = 0$. What is the probability that she is ever swept a full kilometer below her put-in point — that $X_t$ ever hits $-1$?