Let V_r be Ritu's speed in still water. Let V_s# be the stream's speed. Downstream, the 2 speeds help each other.
(V_r + V_s)*2 hrs = 20 km
Upstream, the 2 speeds are in opposite directions.
(V_r - V_s)*2 hrs = 4 km
Multiply the 2 hrs through the parentheses in both expressions.
V_r*2 hrs + V_s*2 hrs = 20 km
V_r*2 hrs - V_s*2 hrs = 4 km
Solve both expressions for the V_r*2 hrs terms and then set the 2 expressions that are equal to V_r*2 hrs instead equal to each other.
V_r*2 hrs = -V_s*2 hrs + 20 km
V_r*2 hrs = V_s*2 hrs + 4 km
Therefore,
-V_s*2 hrs + 20 km = V_s*2 hrs + 4 km
Solve for V_s.
16 km = V_s*2 hrs + V_s*2 hrs = V_s*4 hrs
V_s*4 hrs = 16 km
V_s = (16 km)/(4 hrs) = 4 (km)/(hr)
Just for fun, what is Ricu's speed in still water?
V_r*2 hrs + V_s*2 hrs = 20 km
V_r*2 hrs + 4 (km)/(hr)*2 hrs = 20 km
V_r*2 hrs = 20 km - 4 (km)/(hr)*2 hrs = 20 km - 8 km = 12 km
V_r = (12 km)/(2 hrs) = 6 (km)/(hr)
I hope this helps,
Steve
