Answer:
Let x be the speed of current ( miles per hour ),
Thus, as per statement,
The speed of boat in still water = 5x miles per hour,
⇒ The speed in upstream = 5x - x = 4x miles per hour,
And, the speed in downstream = 5x + x = 6x miles per hour,
We know that,
[tex]Time = \frac{Distance}{Time}[/tex]
Given distance = 12 miles,
So, the time taken in upstream = [tex]\frac{12}{4x}=\frac{3}{x}\text{ hour}[/tex]
And, the time taken in downstream = [tex]\frac{12}{6x}=\frac{2}{x}\text{ hours}[/tex]
Total time taken = 2½ hours
[tex]\implies \frac{3}{x}+\frac{2}{x}=2\frac{1}{2}[/tex]
[tex]\implies \frac{5}{x}=\frac{5}{2}[/tex]
[tex]\implies x = 2[/tex]
Hence, the speed of current is 2 miles per hour.
