Question

Two rowers, who can row at the same speed in still water, head across a river.

The first rower (Alice) heads straight across (but of course her boat is pulled downstream by the current).

The second rower (Bianca) heads slightly upstream, so that with the pull of the current she arrives directly opposite their starting point.

Who arrives at the other side first?

A) Alice
B) Bianca
C) It's impossible to tell without more information.

Answer 1

Alice will arrive first. The downstream pull is independent of the rowing, so the river will be crossed faster if the rower directs all their energy straight across.

This is similar/related to the fact that a bullet fired parallel to the surface of the earth from a gun and a bullet dropped from the same height as the gun will both hit the ground at the same time (assuming no air resistance and that the earth is flat), because the pull of gravity is the same on each of them--the force from the gunshot is independent of the pull of gravity.

This can also be illustrated by vector addition as seen here:

Rowing against river: http://www.wolframalpha.com/input/?i=vector+%7B3%2C+4%7D+%2B+vector+%7B0%2C+-4%7D

Directing full magnitude across river: http://www.wolframalpha.com/input/?i=vector+%7B5%2C+0%7D+%2B+vector+%7B0%2C+-4%7D

(Where the other bank of the river is in the positive x direction.)