Answer: D. 3 miles per hour.
Explanation:
Since, the speed of the boat in still water = 9 mph
Let, x be the speed of the current of the river.
Then, the speed of boat with the river current = 9+x mph
And, speed of boat against the river current = 9-x mph
According to the question,
Total distance with river=total distance against river = 16 miles.
Thus, Time taken by boat with the current= [tex]\frac{16}{9+x}[/tex] ( because time=distance/speed)
And, Time taken by boat against the current= [tex]\frac{16}{9-x}[/tex]
But, total time taken by boat in both with and against the current= 4 hours.
⇒[tex]\frac{16}{9+x}+\frac{16}{9-x}= 4[/tex]
⇒[tex]16(\frac{1}{9+x}+\frac{1}{9-x})= 4[/tex]
⇒[tex]4(\frac{1}{9+x}+\frac{1}{9-x})= 1[/tex]
⇒[tex]4(\frac{1}{81-x^2})= 1[/tex]
⇒[tex]\frac{18}{81-x^2}= 1/4[/tex]
⇒[tex]x^2=9[/tex]⇒[tex]x=\sqrt{9}=3[/tex] ( we will not take -3 value because speed can not be negative)
Therefore, speed of the current of the river= 3mph
