When the boat's speed was $45$ km/h, its engine suddenly stopped.
$7$ minutes after the engine stopped, the boat's speed was $12$ km/h.
It is known that on the boat, in the opposite direction to its movement, the frictional force of the water acts, which is proportional to the speed of the boat.
Find the law of the boat's motion in a river with a constant current of $3$ km/h in the direction of the boat's motion.
After how long will the speed of the boat be $4$ km/h?
My thoughts: $$ \left\{ \begin{array}{c} f'(x)=45-3f(x) \\ f'(7)=45-3f(7)=12 \rightarrow f(7)=11\\ \end{array} \right. $$ $$f(x)=15-4e^{21-3x}$$ so $$ f'(x)=12e^{21-3x}$$ and we need to solve $$f'(x)=4$$ so $$12e^{21-3x}=4 \rightarrow x=7+\frac{\ln(3)}{3} = 7.366$$