Paddle boat

Question

A paddle boat can move at a speed of 14 km/h in still water. The boat is paddled 4 km downstream in a river in the same time it takes to go 2 km upstream. What is the speed of the river?

Answer 1

Remember, that distance = rate times time or D=rt.  This can be rewritten as t = D/r.

 

Let x = speed of the river.

 

The speed going downstream will be 14 + x since the river is helping the boat move, and the speed going upstream will be 14 - x since the river is going against the boat.

 

The time downstream can be modeled by 4/(14+x) while the time upstream can be modeled by 2/(14-x).  Setting these values equal allows you to solve for the rate of the river.

 

4/(14+x)=2/(14-x)

4(14-x)=2(14+x)

56-4x=28+2x

56=28+6x

28=6x

4.7≈x

 

The river is traveling approximately 4.7 km/h.