  Let $(S_t)_{t\geq 0}$ be the running maximum of a standard Brownian motion
$(B_t)_{t\geq 0}$ and $T_m:=\inf\{t; \, mS_t<t\},\, m>0$. In this note we
calculate the joint distribution of $T_m$ and $B_{T_m}$. The motivation for our
work comes from a mathematical model for animal foraging. We also present
results for Brownian motion with drift.
