let

b = the rate of the boat in still water

c = the rate of the current

t = 6 hr the time of the travel in one direction

d1 = 217 km the distance of the trip upstream

d2 = 413 km the distance of the trip downstream

the rate of the boar traveling upstream is: b - c

the rate of the boar traveling downstream is: b + c

since the rate = distance/time => distance = time*rate

traveling upstream

d1 = (b - c)*t

(b - c)*t = d1

(b - c)*7 = 217 divide both sides by 7

b - c = 31

traveling downstream

d2 = (b + c)*t

(b + c)*t = d2

(b + c)*7 = 413 divide both sides by 7

b + c = 59

by solving the system of equations

b - c = 31

b + c = 59

we find

b = 45 mph

c = 14 mph

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

the rate of the boat in still water is 45 mph.

the rate of the current is 14 mph.