Answer
It takes 14.3 seconds for the motorboat to make the crossing.
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
We can convert the speed $v_m$ to units of ft/s:
$6.3~mph\times \frac{1~h}{3600~s}\times \frac{5280~ft}{1~mi} = 9.24~ft/s$
The distance across the river is 132 feet. We can find the time it takes the motorboat to make the crossing:
$t = \frac{132~ft}{9.24~ft/s} = 14.3~s$
It takes 14.3 seconds for the motorboat to make the crossing.
