Answer
Relative to the banks, the motorboat will be traveling at a speed of 6.3 mph
Work Step by Step
Let $v_b$ be the speed of the motorboat in still water.
Let $v_c$ be the speed of the current.
Let $v_m$ be the actual speed of the motorboat. Note that the vector $v_m = v_b+v_c$
These three vectors form a right triangle where $v_b$ is the hypotenuse.
We can find $v_m$:
$v_m^2 = v_b^2-v_c^2$
$v_m = \sqrt{v_b^2-v_c^2}$
$v_m = \sqrt{(7.0~mph)^2-(3.0~mph)^2}$
$v_m = \sqrt{40.0~mph^2}$
$v_m = 6.3~mph$
Relative to the banks, the motorboat will be traveling at a speed of 6.3 mph
