For drifted Brownian motion X(t) = x − µt + B t (µ > 0) starting from x > 0, we study the joint distribution of the first-passage time below zero, τ (x), and the first-passage area, A(x), swept out by X till the time τ (x). In particular, we establish differential equations with boundary conditions for the joint moments E[τ (x) m A(x) n ], and we present an algorithm to find recursively them, for any m and n. Finally, the expected value of the time average of X till the time τ (x) is obtained.