I don't understand the idea of perpendicular vectors being independent of each other? So problem 71-75 is about vectors. The problem says:

A river has a current flowing with a velocity of 2.0 meters per second due east. A boat is 75 meters from the north riverbank. It travels at 3.0 meters per second relative to the river and is headed due north. In the diagram below, the vector starting at point P represents the velocity of the boat relative to the river water. 

http://www.jmap.org/JMAP/IJMAP/Physics/RegentsExams/0612ExamPH.pdf
Then it says, 

Calculate the time required for the boat to cross the river.

Apparently I'm suppose to d=vt where d = 75m, v = 3.0m/s and solve for t. Why is it that I use 3.0 m/s and not sqrt(13) m/s which is the resultant? 
I know it says that perpendicular vectors are independent of each other but that doesn't really make sense to me.  If I'm crossing some distance and I'm getting pushed horizontally, then I'd be travelling diagonally which is a longer distance then a vertical distance? 
Also what does "relative to the river" in the problem? 
 A: ""I don't understand the idea of perpendicular vectors being independent of each other?..""   
I'll take this as your question; the homework part you can work on yourself.
You probably understand that any vector can be replaced by two component vectors that are at right angles to each other, and form a closed right triangle.   So for example a force vector of 10 units at 30 degrees above the horizontal axis, can be resolved into an 8.66 force vector along the X axis, and a 5.0 force vector along the Y axis.   So the original vector produces those effects on the two axes.
But if my 10 units force vector is pointing directly along the X axis, then the resolved Y component is 10 sin(0) = 0  So the  the force 10 along the X axis produces zero force along the Y axis, and conversely, if it pointed along Y instead, the component along X would be zero.    So any vector produces NO effect in a direction perpendicular to it.  Ergo they are independent, if perpendicular.
Now you should be able to do your homework problem.
A: It's pretty simple really. The problem here is that you're considering 75 m to be the diagonal distance traveled whereas it is actually the distance ACROSS the river. Should the distance provided to you have been the diagonal displacement of the object, you would use the resultant velocity to find the time taken. However, taking into account the independence of perpendicular vectors, you may simply take the horizontal component and divide the horizontal displacement by it.
