The speed of the stream: v s = 1 mph
v - Davids speed in still water
( v - 1 ) t 1 = 3
( v + 1 ) t 2 = 3
t 1 + t 2 = 4
---------------------------
t 2 = 4 - t 1
3 = ( v - 1 ) t 1
3 = ( v + 1 ) ( 4 - t 1 )
-----------------------------
3 = v t 1 - t 1
+
3 = 4 v - v t 1 + 4 - t 1
------------------------------
6 = 4 v + 4 - 2 t 1
2 = 4 v - 2 t 1
2 t 1 = 4 v - 2 / : 2 ( divide both sides of equation by 2)
t 1 = 2 v - 1
t 2 = 5 - 2 v
------------------
3 = ( v - 1 ) * ( 2 v - 1 )
3 = 2 v² - 3 v + 1
2 v² - 3 v - 2 = 0
v 1/2 = 3+/- √(9 + 16 ) / 4 = (3 + 5)/4 = 8/4 = 2 ( other solution is negative )
Answer: Davids speed in still water is 2 miles per hour.
