let

v = the rate of the boat in still water

c = the rate of the current

t1 = 4 hr time of the travel upstream

d = 192 mi upstream travel distance

t2 = 3 hr the time of the return trip downstream

the boats speed downstream: v + c

the boats speed upstream: v - c

since speed = distance/time we have

travelling downstream

v + c = d/t2

v + c = 192/3

v + c = 64

travelling upstream

v - c = d/t1

v - c = 192/4

v - c = 48

by solving the system of equations

v + c = 64

v - c = 48

we find

v = 56 mph

c = 8 mph

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

the rate of the boat in still water is 56 miles per hour.

the rate of the current is 8 miles per hour.