Answer
Resultant velocity of the boat is 5 miles per hour.
Work Step by Step
The model situation in plane $\mathbb{R}^2$
$Unit \;vectotrs\; is\; \overrightarrow{a}\;=(0,1)\; from\;North\;\;\;\;\;\;\;and\;\;\;\;\;\;\overrightarrow{b}\;=(1,0)\;from\;East\\\\$
When wind blows:
$4\;\overrightarrow{a}\;+\;3\;\overrightarrow{b}\;=\;4(0,1)\;+\;3(1,0)\;=\;(0,4)\;+\;(3,0)\;=\;(3,4)\\\\$
The velocity of the plane:
$\left \| 4\;\overrightarrow{a}\;+\;3\;\overrightarrow{b} \right \|\;=\;\sqrt{3^2\;+\;4^2}\;=\;5\\\\$
Resultant velocity of the boat is 5 miles per hour.
