let

v = 25 mph the speed of the boat in still water, v>0

c = speed of the current

d1 = 136 miles the distance he travels with the current

d2 = 64 miles the distance he travels against the current

t = the time of the travel upstream = the time of the travel downstream

traveling with the current speed: v + c

traveling against the current speed: v - c

since speed = distance/time we have time = distance/speed

traveling with the current

t = d1/(v + c)

t = 136/(25 + c)

traveling against the current

t = d2/(v - c)

t = 64/(25 - c)

by solving the equation

136/(25 + c) = 64/(25 - c)

we find

c = 9 mph

click here to see the step by step solution of the equation:

the speed of the current is 9 mph.