Mary needs to row her boat across a 200m wide river that is flowing to the east at a speed of 1.4m/s . mary can row with a speed of 2.2m/s what is her speed with respect to the shore?

The problem you provided can be solved using the concept of relative motion. 

Her velocity has the components of 1.4m/s N and 2.2 m/s E so the net velocity has magnitude; 

v = Sqrt(2.2^2 + 1.4^2) = Sqrt(6.8)

Therefore, the speed of Mary with respect to the shore is Sqrt(6.8) meters per second.

I hope it has come to your help.