Answer
The average velocity of the boat in still water is $4.5$ mph and that of the current is $1.5$ mph.
Work Step by Step
Step 1. Assume the average velocity of the boat in still water is $x$ mph and that of the current is $y$ mph.
Step 2. When traveling with the stream, the total average velocity is $x+y$, thus $4(x+y)=24$ or $x+y=6$
Step 3. When traveling against the stream, the resulting average velocity is $x-y$; thus $6(x-y)=24\times(\frac{3}{4})$ or $x-y=3$
Step 4. Adding the two equations, we get $2x=9$; thus $x=4.5$ and $y=1.5$ mph.
