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
