(a) A Boat is paddling upstream at 1.25 m/s relative to the water in a river which is flowing at 0.50 m/s relative to the banks of the river.What...

This is a fairly straightforward vector problem. Imagine
for a moment that Rosa stops paddling, and think about what that would look like to you
if you were standing on the bank. Rosa, now floating with the current, would be going
past you at 0.5 m/s, wouldn't she?

Now for a different
picture. If the river had zero current and Rosa paddled past you, she would be going
1.25 m/s.

The motions of Rosa and the river do not depend
on each other. Because they are both going in the same direction, you can just add them
up. Rosa's actually going downstream at 0.5 + 1.25 = 1.75
m/s.

Just for the record, if Rosa was paddling
upstream (against the current)  we would subtract the two speeds
because they would partially cancel each other out.

The
link below explains how to do these problems with vector diagrams, which may help you to
picture them more clearly.