let

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

s = 6 mph the speed of the stream

d1 = 83 mi traveling downstream

d2 = 35 mi traveling upstream

traveling downstream the speed of the boat is: v + s

traveling upstream the speed of the boat is: v - s

since speed = distance/time we have time = distance/speed we have

the time going downstream = the time going upstream

d1/(v + s) = d2/(v - s)

63/(v + 6) = 35/(v - 6)

by solving we find:

v = 21 mph

click here to see the step by step solution of the equation:

the speed of the boat in still water is 21 miles per hour.