let

v = 3 mph the rate of the boat in still water

t = 3 hr 36 min = 3 + 36/60 hr = 3.6 hr the time of the travel (upstream and return)

d = 3 mi the distance in one direction

c = the rate of the water's current

the rate of the boat traveling downstream is: v + c

the rate of the boat traveling upstream is: v - c

since rate = distance/time we have time = distance/rate

d/(v - c) + d/(v + c) = t

3/(3 - c) + 3/(3 + c) = 3.6

by solving we find:

c = 2 mph

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

the speed of the current is 2 mph.