We will use distance formula which states:
[tex] d=r \times t [/tex]
where 'd' is the distance, 'r' is rate or speed and 't' is time taken.
So, [tex] t=\frac{d}{r} [/tex]
Let 'u' be the speed of boat in still water.
A person rows 14 miles downstream to the fishing spot.
So, the speed of boat downstream = (u+6) mph
Time taken by boat to go downstream = [tex] \frac{14}{u+6} [/tex] hr
He rows 2 miles upstream from the fishing spot.
So, the speed of boat upstream = (u-6) mph
Time taken by boat to go upstream = [tex] \frac{2}{u-6} [/tex] hr
Since, The person took same amount of time in going downstream and then going upstream.
So, [tex] \frac{14}{u+6}=\frac{2}{u-6} [/tex]
Cross multiplying, we get
[tex] 14 (u-6)= 2(u+6) [/tex]
[tex] 14u - 84 = 2u + 12 [/tex]
[tex] 12u = 96 [/tex]
u = 8
So, speed of boat in still water is 8mph.
Now, Time taken in going downstream = [tex] \frac{14}{u+6} [/tex]
= [tex] \frac{14}{8+6} [/tex]
= 1 hr
Now, Time taken in going upstream = [tex] \frac{2}{u-6} [/tex]
= [tex] \frac{2}{8-6} [/tex]
= 1 hr
So, total time taken to cover 16 miles is 2 hours.
