Distance = Velocity * time

let

b = speed of boat in still water

Upstream

8 = (b - 4)t

Downstream

16 = (b + 4)t

Double the Upstream equation

16 = 2(b - 4)t

Since both equations equal 16 set them equal

(b + 4)t = 2(b - 4)t

Divide both sides by t

b + 4 = 2(b - 4)

b + 4 = 2b - 8

Subtract b from both sides

4 = b - 8

Add 8 to both sides

12 = b

The speed is 12 mph

m07202013

4 mph is the speed of the stream.  That means is the stream affects the boat 4 mph in both directions.  (That's 8 mph total.) The boat goes a total of 8 actual + 4 against the stream upstream = 12 mph.

And it goes 16 actual -  4 with the stream downstream = 12 mph

Note: it must be one hour because the difference is 8 miles    

So The speed is 12 mph