Answer
The average velocity of the boat in still water is $6.25$ mph and that of the current is $1.75$ 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 $3(x+y)=24$ or $x+y=8$
Step 3. When traveling against the stream, the resulting average velocity is $x-y$; thus $4(x-y)=24(3/4)$ or $x-y=\frac{9}{2}$
Step 4. Adding the two equations, we get $2x=\frac{25}{2}$; thus $x=\frac{25}{4}=6.25$ and $y=1.75$.
