Motion Along a Straight Line: Calculate velocity of a stream

[alexsphysics]

Homework Statement

A swimmers speed along the river is 20 km/h and upstream is 8 km/h. Calculate the velocity of the stream and the swimmers possible speed in still water

Relevant Equations

I understand what the variables are and I understand what it is asking to find, but what I'm having trouble with is putting together an equation/formula that will help solve the problem.

Not sure how to go about it

 

[HallsofIvy]

Assuming that the swimmer is swimming at the same speed relative to the water then, writing "u" for the speed of the swimmer, relative to the water and "v" for the speed of the water, then u+ v= 20 and u- v= 8. If you subtract the second equation from the first, 2v= 12 so v= 6 km/h.

 

[alexsphysics]

Why does u-v=8?

 

[HallsofIvy]

Swimming upstream the swimmer is moved backward by the current. If his speed relative to the water is u and the speed of the water is v, then his speed relative to the bank is u- v. In your first post you said "A swimmers speed along the river is 20 km/h and upstream is 8 km/h" so u- v= 8 km/h.

 

[alexsphysics]

Yes, that is much more simple that I sought out the problem to be for some reason. Thanks a lot!