@PsiSquared I think we're perceiving the problem differently. To both of you, here's what I think. See what you think of what I think!
First I'll look at it from an informal point of view, then I'll use vector reasoning as
@PsiSquared did.
So, the boat is only propelling itself westward. But it is still going downstream. The boat propels itself westward, and so it moves west relative to the water (the body it's propelling itself within). That, what is relative to the water, is what the speedometer is reading (\(30\rm\ km/hr\ west\))*. It is moving downstream, but \(\rm with\) the water. So the speedometer does not pick up on that. It's downstream velocity, since the boat does not propel itself downstream or upstream, is just going to be the velocity of the water (\(5\rm\ km/hr\ south\))**. Thus, its total velocity*** can be found by vector-adding the two velocities. Since south is perpendicular to west, the velocities are orthogonal, and so the magnitude (like length) of their vector sum can be found by the Pythagorean theorem.
* With respect to water and ground
** With respect to ground. (It's zero, or still, with respect to water)
*** With respect to ground
I'll post this so that I don't lose it! If there are errors in it, please let me know! I will proceed to make a visual for the vector additions for this problem and the plane scenario that
@PsiSquared introduced!