let me try my hand at explaining.

So the figure will give u the necessary info. 'bout the river and the boat

The river having a velocity u and the boat a velocity v making an angle  with the vertical.

So the velocity of the boat in the vertical direction becomes vcos and that in the horizontal direction becomes

u + vsin as the boat acquires the velocity of the river.

So time for crossing the river t = (width of river) / (relative velocity of boat w.r.t. river in vertical direction)

i hope this is clear.

So t = d / v.cos 

and x = (rel. vel. of boat w.r.t. river in horizontal dir.) x t 

= (u + v.sin) x (d / vcos) = {(u + v.sin) / (v.cos)} x d

and now u can thereby easily get the conditions for crossing the river in minimum time and to reach the point exactly opposite to point of starting.

For minimum time, v.cos should be maximum, so cos = 1 i,e,  = 0⁰.

and for reaching the point exactly opposite to point of starting, x = 0. So, u + v.sin = 0 i,e sin = -u/v ... which is possible iff u < v.