Ritu can row downstream 20 kms in 2 hours and upstream 4 km in 2 hours. What is the speed of the current ?

1 Answer
Jan 26, 2018

The speed of the current is 4 (km)/(hr)4kmhr.

Explanation:

Let V_rVr 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(Vr+Vs)2hrs=20km

Upstream, the 2 speeds are in opposite directions.

(V_r - V_s)*2 hrs = 4 km(VrVs)2hrs=4km

Multiply the 2 hrs through the parentheses in both expressions.
V_r*2 hrs + V_s*2 hrs = 20 kmVr2hrs+Vs2hrs=20km
V_r*2 hrs - V_s*2 hrs = 4 kmVr2hrsVs2hrs=4km

Solve both expressions for the V_r*2 hrsVr2hrs terms and then set the 2 expressions that are equal to V_r*2 hrsVr2hrs instead equal to each other.
V_r*2 hrs = -V_s*2 hrs + 20 kmVr2hrs=Vs2hrs+20km
V_r*2 hrs = V_s*2 hrs + 4 kmVr2hrs=Vs2hrs+4km

Therefore,
-V_s*2 hrs + 20 km = V_s*2 hrs + 4 kmVs2hrs+20km=Vs2hrs+4km

Solve for V_sVs.
16 km = V_s*2 hrs + V_s*2 hrs = V_s*4 hrs16km=Vs2hrs+Vs2hrs=Vs4hrs
V_s*4 hrs = 16 kmVs4hrs=16km

V_s = (16 km)/(4 hrs) = 4 (km)/(hr)Vs=16km4hrs=4kmhr

Just for fun, what is Ricu's speed in still water?
V_r*2 hrs + V_s*2 hrs = 20 kmVr2hrs+Vs2hrs=20km

V_r*2 hrs + 4 (km)/(hr)*2 hrs = 20 kmVr2hrs+4kmhr2hrs=20km

V_r*2 hrs = 20 km - 4 (km)/(hr)*2 hrs = 20 km - 8 km = 12 kmVr2hrs=20km4kmhr2hrs=20km8km=12km

V_r = (12 km)/(2 hrs) = 6 (km)/(hr)Vr=12km2hrs=6kmhr

I hope this helps,
Steve