How fast is the river?

Question

A paddleboad can move at a speed of 2 km/h in still water. the boad is paddled 10 km downstream in a river in the same time it takes to go 5 km upstream. What is the speed of the river?

Answer 1

Hi Collin,

 

distance = speed * time

 

let x = speed of the current  (we will add x to our overall speed we are going with the current and subtract against the current

 

speed downstream = 2 + x

 

speed upstream = 2 - x

 

5 = (2-x)*t

 

10 = (2+x)*t

 

solve for t first

 

t = 5/(2-x)

 

t = 10/(2+x)   

 

since the t is the same for both trips, we can now set these two equal

 

5/(2-x)=10/(2+x)

 

cross multiply

 

10 + 5x = 20 - 10x

 

15x = 10

 

x = 2/3 km/h

 

Hope this helps