We have been given that the upstream speed is [tex]5 mph[/tex] and the down stream speed is [tex]10mph[/tex].
Let the fisherman traveled a distance of x miles.
The total time of the trip is 6 hours.
Relations between speed (s), time (t) and distance (d) is [tex]s = \frac{d}{t}[/tex]
Hence, [tex]t= \frac{d}{s}[/tex]
Time upstream + time downstream = 6
[tex]\frac{x}{5} +\frac{x}{10} =6[/tex]
lcm = 10
[tex]\frac{2x+x}{10} =6[/tex]
=> [tex]\frac{3x}{10} =6[/tex]
Cross multiplying, [tex]3x= 60[/tex]
x = 20 miles .. Answer.