let

b = the rate of the boat in still water

c = the rate of the current

t1 = 5 hr the time of the travel upstream

d = 150 mi the distance of the trip on one direction

t2 = 3 hr the time of the travel 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

(b - c)*t1 = d

(b + c)*t2 = d

of if we plug the values

(b - c)*5 = 150 divide both sides by 5

b - c = 30

(b + c)*3 = 150 divide both sides by 3

b + c = 50

by solving the system of equations

b - c = 30

b + c = 50

we find

b = 40 mph

c = 10 mph

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

the rate of the boat in still water is 40 mph.

the rate of the current is 10 mph.