let

d1 = 72 mi the distance traveled downstream

t1 = 3 hr the time of the travel downstream

d2 = 60 mi the distance traveled upstream

t2 = 6 hr the time of the travel upstream

v = rate of the boat in still water, v>0

r = the rate of the river

we know that speed = distance/time

traveling downstream the rate of the boat is v + r

(v + r) = d1/t1

(v + r) = 72/3

traveling upstream the rate of the boat is v - r

(v - r) = d2/t2

(v - r) = 60/6

by solving the system of equations:

(v + r) = 72/3

(v - r) = 60/6

we find:

v = 17 mph

r = 7 mph

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

(v - r) = 60/6

the rate of the river is 7 mph.

the rate of the boat in still water is 17 mph.