let

v = the speed of the boat in still water

s = 5 mph the speed of a stream

d1 = 5 mi the distance traveled upstream

d2 = 15 mi the distance traveled downstream

t = the time of the travel on one direction

the boats speed downstream: v + s = v + 5

the boats speed upstream: v - s = v - 5

since speed = distance/time we have

traveling upstream

v - 5 = 5/t multiply both sides by t

vt - 5t = 5

vt = 5 + 5t

traveling downstream

v + 5 = 15/t multiply both sides by t

vt + 5t = 15

plug vt = 5 + 5t into the last equation

5 + 5t + 5t = 15

by solving we find

t = 1 hr

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

v + 5 = 15/1

v = 15 - 5

v = 10 mph

the speed of the boat in still water is 10 mph.