Let the speed of the current of the river be = x
And, the speed of the boat in still water = 9 mph
Then, the speed of boat along the river current will be= 9+x mph
And, speed of boat against the river current will be = 9-x mph
Now as given, total distance along river current and total distance against river current is same = 16 miles.
As we know, time=distance/speed
Time taken by boat along the river current = [tex]\frac{16}{9+x}[/tex]
And time taken by boat against the river current = [tex]\frac{16}{9-x}[/tex]
Also given is , the overall the journey takes 4 hours; so equation becomes
[tex]\frac{16}{9+x}+\frac{16}{9-x}=4[/tex]
[tex]4(\frac{1}{9+x}+\frac{1}{9-x})=1[/tex]
Solving this we get; [tex]x^{2} =9[/tex] or x=3
Therefore, the speed of the current of the river is 3 mph.
