what is the speed of the river

Question

a paddleboat can move at a speed of 2 km/hour in still water.  The boat is paddeled 16km downstream in a river in the same time it takes to go 8km upstream.  What is the speed of the river?

Answer 1

Distance = Rate times Time  

 

Let S be the speed of the river 

Then the boat paddles downstream at (2 + S) km/hour  

And the boat goes upstream at (2 - S) km/hour  

 

Let T be the time (same upstream and downstream)  

 

So the equations are  

 

16 = (2 + S)*T = 2*T + S*T  downstream  

 8  = (2 - S)*T  = 2*T -  S*T  upstream  

 

Add these 2 equations together to get 

 

24 = 4*T 

T = 6 

 

Plug this value for T back in to the 1st equation to solve for S  

 

16 = (2 + S)*6

2 + S = 8/3

S = 2/3 

 

The speed of the river is 2/3 km/hour  

 

Check:  Downstream speed = 2 + 2/3 = 8/3 km/hour

            Downstream distance = (8/3)*6 = 16 km 

            Upstream speed = 2 - 2/3 = 4/3 km/hour 

            Upstream distance = (4/3)*6 = 8 km