D=RT question

Question

The question is:

 

Annette's paddleboat travels 2km/h in still water. The boat is paddled 4km downstream in the same time it takes to go 1 km upstream. What is the speed of the river?

 

 

How do I solve this? Thank you.

Answer 1

Let X = speed of the river 

 

Then rate downstream = 2 + X

 and  rate  upstream    = 2 - X  

 

D=RT  ==>  T = D/R

 

The downstream equation is T = 4/(2+X)

The  upstream    equation is T = 1/(2-X) 

 

The two times are equal, so 

 

4/(2+X) = 1/(2-X) 

2+X = 4(2-X) = 8 - 4X

5X = 6

X = 6/5 km/h is the speed of the river 

 

Check:  Downstream T = 4/[2+(6/5)] = 4/(16/5) = 20/16 = 5/4 h

            Upstream T = 1/[2-(6/5)] = 1/(4/5) = 5/4 h