let

v = the speed of the boat in still water

w = the speed of the current

t1 = 5 hr the time of the paddling with the current

v + w = 3 km/h the speed of the paddling with the current

t2 = 8 hr the time for the paddling against the current

since he paddled the same distance in each direction and speed = distance*time we have:

(v + w)t1 = (v - w)t2

3*5 = (v - w)*8

(v - w)*8 = 15

by solving the system of equations:

v + w = 3

(v - w)*8 = 15

we find:

v = 2.44 km/h

w = 0.56 km/h

click here to see the step by step solution of the system of equations:

the speed of the boat in still water is 2.44 km/h.